{"group":{"group":{"id":91051,"name":"Prime Numbers III","lockable":false,"created_at":"2024-07-04T22:01:20.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"More problems on the building blocks of numbers","is_default":false,"created_by":46909,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":17,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":6631,"published":true,"community_created":true,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore problems on the building blocks of numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 290px 10.5px; transform-origin: 290px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 267px 10.5px; text-align: left; transform-origin: 267px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.883px 8px; transform-origin: 152.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMore problems on the building blocks of numbers\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2024-07-04T22:15:45.000Z"},"current_player":null},"problems":[{"id":52664,"title":"List the Moran numbers","description":"The quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \r\nWrite a function to list the Moran numbers less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363px 8px; transform-origin: 363px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257px 8px; transform-origin: 257px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the Moran numbers less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Moran(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 500;\r\ny = Moran(n);\r\ny_correct = [18 21 27 42 45 63 84 111 114 117 133 152 153 156 171 190 195 198 201 207 209 222 228 247 261 266 285 333 370 372 399 402 407 423 444 465 481];\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nn = 40332;\r\ny = Moran(n);\r\ny23_correct = [207 1679 3749 4577 8717 14099 18653 19067 22793 24449 25691 26519 26933 29417 29831 32729 33557 35627 37283];\r\nassert(isequal(y(mod(y,23)==0),y23_correct) \u0026\u0026 isequal(y(end),n))\r\n\r\n%%\r\nn = [100000 400000 700000 1e6 4e6 7e6 1e7];\r\ns = [383 1193 1870 2451 8080 12913 17271];\r\nlen_correct = [1915 5967 9352 12259 40403 64567 86356];\r\nsum_correct = [79699686 1044807776 2880495403 5339917218 73480226594 205122929098 389309242207];\r\nsd_correct  = [2.925215086021406e+04 1.171076738381341e+05 2.065163622127620e+05 2.944277010513903e+05 1.177431499460555e+06 2.057551640570258e+06 2.933705654924581e+06];\r\nys_correct  = [11354 28489 48992 71660 99972; 51489 125203 210051 300165 399477; 96325 220734 364473 524186 699739; 129627 308214 513837 741778 999219; 579189 1331117 2176042 3062214 3999644; 1046322 2330397 3782883 5322552 6999255; 1440693 3292137 5341677 7565613 9999882];\r\nfor k = 1:length(n)\r\n    disp(['Test 3.' num2str(k)])\r\n    y = Moran(n(k));\r\n    assert(isequal(length(y),len_correct(k)) \u0026\u0026 isequal(sum(y),sum_correct(k)) \u0026\u0026 abs(std(y)-sd_correct(k))\u003c1e-7 \u0026\u0026 isequal(y(s(k):s(k):end),ys_correct(k,:)));\r\nend\r\n\r\n%%\r\nfiletext = fileread('Moran.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-05T13:52:35.000Z","updated_at":"2025-12-15T19:21:34.000Z","published_at":"2021-09-05T14:10:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the Moran numbers less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52881,"title":"List the cuban primes","description":"The number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \r\nWrite a function to list the cuban primes less than or equal to the input number. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 295.108px 8.05px; transform-origin: 295.108px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 245.3px 8.05px; transform-origin: 245.3px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the cuban primes less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8.05px; transform-origin: 0px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function q = cubanPrimes(n)\r\n  q = n^3;\r\nend","test_suite":"%%\r\nn = 100;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 1000;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61 127 271 331 397 547 631 919];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 10000;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61 127 271 331 397 547 631 919 1657 1801 1951 2269 2437 2791 3169 3571 4219 4447 5167 5419 6211 7057 7351 8269 9241];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 100000;\r\nq = cubanPrimes(n);\r\nqhi_correct = [10267 11719 12097 13267 13669 16651 19441 19927 22447 23497 24571 25117 26227 27361 33391 35317 42841 45757 47251 49537 50311 55897 59221 60919 65269 70687 73477 74419 75367 81181 82171 87211 88237 89269 92401 96661];\r\nassert(isequal(q(q\u003e10000),qhi_correct))\r\n\r\n%%\r\nn = 1e6;\r\nq = cubanPrimes(n);\r\nqhi_correct = [102121 103231 104347 110017 112327 114661 115837 126691 129169 131671 135469 140617 144541 145861 151201 155269 163567 169219 170647 176419 180811 189757 200467 202021 213067 231019 234361 241117 246247 251431 260191 263737 267307 276337 279991 283669 285517 292969 296731 298621 310087 329677 333667 337681 347821 351919 360187 368551 372769 374887 377011 383419 387721 398581 407377 423001 436627 452797 459817 476407 478801 493291 522919 527941 553411 574219 584767 590077 592741 595411 603457 608851 611557 619711 627919 650071 658477 666937 689761 692641 698419 707131 733591 742519 760537 769627 772669 784897 791047 812761 825301 837937 847477 863497 879667 886177 895987 909151 915769 925741 929077 932419 939121 952597 972991 976411 986707 990151 997057];\r\nassert(isequal(q(q\u003e100000),qhi_correct))\r\n\r\n%%\r\nn = 1e7;\r\nq = cubanPrimes(n);\r\nqhi = q(q\u003e1e6);\r\nqhi26_correct = [1021417 1570357 2129419 2676241 3483019 4476187 5382781 6138991 7073281 8401807 9779491];\r\nassert(isequal(qhi(1:26:end),qhi26_correct))\r\n\r\n%%\r\nn = 1e8;\r\nq = cubanPrimes(n);\r\nlen_correct = 1200;\r\nqhi20_correct = [67987081 71282251 74326519 77892361 81510469 84891241 88210519 92991169 95954041 99896011];\r\nassert(isequal(q(1020:20:end),qhi20_correct) \u0026\u0026 isequal(length(q),len_correct))\r\n\r\n%%\r\nn = 1e9;\r\nq = cubanPrimes(n);\r\ns = sum(q(primes(length(q))));\r\ns_correct = 127462233426;\r\nqmax_correct = 999461269;\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(max(q),qmax_correct))\r\n\r\n%%\r\nfiletext = fileread('cubanPrimes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin') || contains(filetext, 'persistent');\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2021-10-10T13:54:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-10T13:40:55.000Z","updated_at":"2025-12-14T17:50:30.000Z","published_at":"2021-10-10T13:52:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the cuban primes less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52956,"title":"Compute the largest number whose prime factors sum to n","description":"This problem deals with a sequence whose tenth term is 36 because the prime factors of 36 (2, 2, 3, 3) sum to 10. The number 32 would also fit, but the elements of this sequence are the largest possible examples. \r\nWrite a function to produce the th term in this sequence. In other words, compute the largest number whose prime factors sum to . Take the first term in the sequence to be 1. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.325px 8.05px; transform-origin: 368.325px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with a sequence whose tenth term is 36 because the prime factors of 36 (2, 2, 3, 3) sum to 10. The number 32 would also fit, but the elements of this sequence are the largest possible examples. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.1083px 8.05px; transform-origin: 97.1083px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to produce the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 280.042px 8.05px; transform-origin: 280.042px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in this sequence. In other words, compute the largest number whose prime factors sum to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.058px 8.05px; transform-origin: 138.058px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Take the first term in the sequence to be 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sopfEqualsN(n)\r\n  y = sum(factor(n));\r\nend","test_suite":"%%\r\nn = 1;\r\ny = sopfEqualsN(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5;\r\ny = sopfEqualsN(n);\r\ny_correct = 6;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 10;\r\ny = sopfEqualsN(n);\r\ny_correct = 36;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11;\r\ny = sopfEqualsN(n);\r\ny_correct = 54;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 13;\r\ny = sopfEqualsN(n);\r\ny_correct = 108;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 17;\r\ny = sopfEqualsN(n);\r\ny_correct = 486;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 19;\r\ny = sopfEqualsN(n);\r\ny_correct = 972;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 23;\r\ny = sopfEqualsN(n);\r\ny_correct = 4374;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 29;\r\ny = sopfEqualsN(n);\r\ny_correct = 39366;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 31;\r\ny = sopfEqualsN(n);\r\ny_correct = 78732;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 37;\r\ny = sopfEqualsN(n);\r\ny_correct = 708588;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 41;\r\ny = sopfEqualsN(n);\r\ny_correct = 3188646;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 47;\r\ny = sopfEqualsN(n);\r\ny_correct = 28697814;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 53;\r\ny = sopfEqualsN(n);\r\ny_correct = 258280326;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 59;\r\ny = sopfEqualsN(n);\r\ny_correct = 2324522934;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 61;\r\ny = sopfEqualsN(n);\r\ny_correct = 4649045868;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 67;\r\ny = sopfEqualsN(n);\r\ny_correct = 41841412812;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 71;\r\ny = sopfEqualsN(n);\r\ny_correct = 188286357654;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 73;\r\ny = sopfEqualsN(n);\r\ny_correct = 376572715308;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 79;\r\ny = sopfEqualsN(n);\r\ny_correct = 3389154437772;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 83;\r\ny = sopfEqualsN(n);\r\ny_correct = 15251194969974;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 89;\r\ny = sopfEqualsN(n);\r\ny_correct = 137260754729766;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 91;\r\ny = sopfEqualsN(n);\r\ny_correct = 274521509459532;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 97;\r\ny = sopfEqualsN(n);\r\ny_correct = 2470693585135788;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 100;\r\ny = sopfEqualsN(n);\r\ny_correct = 7412080755407364;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nfiletext = fileread('sopfEqualsN.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2021-10-14T11:50:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-14T11:40:34.000Z","updated_at":"2025-12-14T17:54:28.000Z","published_at":"2021-10-14T11:47:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with a sequence whose tenth term is 36 because the prime factors of 36 (2, 2, 3, 3) sum to 10. The number 32 would also fit, but the elements of this sequence are the largest possible examples. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to produce the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in this sequence. In other words, compute the largest number whose prime factors sum to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Take the first term in the sequence to be 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53810,"title":"List the Beatriz numbers","description":"Write a function to find integers  less than or equal to an input value  that solve the equation . The function  gives the sum of divisors of ; for example, . The totient function  counts numbers less than  that are relatively prime to . For example,  because 1, 2, 4, 7, 8, 11, 13, and 14 are relatively prime to 15; that is, the greatest common divisor of 15 and each of the eight numbers is 1. \r\nAn oblique hint is that I call solutions to  “Beatriz numbers” in honor of a good friend and former co-worker of EmilyR and JessicaR. The natural search will not help, unless you are interested in combinatorics related to Higham’s conjecture.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 156px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 78px; transform-origin: 407.5px 78px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 42px; text-align: left; transform-origin: 384.5px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.275px 7.66667px; transform-origin: 98.275px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.417px 7.66667px; transform-origin: 112.417px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e less than or equal to an input value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.2917px 7.66667px; transform-origin: 74.2917px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that solve the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sigma(n-1) = phi(n+1)\" style=\"width: 127px; height: 18.5px;\" width=\"127\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8833px 7.66667px; transform-origin: 17.8833px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sigma(x)\" style=\"width: 30.5px; height: 18.5px;\" width=\"30.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.8917px 7.66667px; transform-origin: 31.8917px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gives the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46898\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003esum of divisors\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 7.66667px; transform-origin: 9.71667px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 7.66667px; transform-origin: 44.3333px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; for example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sigma(15) = 1+3+5+15 = 24\" style=\"width: 178.5px; height: 18.5px;\" width=\"178.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.8833px 7.66667px; transform-origin: 17.8833px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/656\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003etotient function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.66667px; transform-origin: 1.94167px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi(x)\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.5px 7.66667px; transform-origin: 24.5px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e counts numbers less than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 7.66667px; transform-origin: 84.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that are relatively prime to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.6667px 7.66667px; transform-origin: 46.6667px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi(15) = 8\" style=\"width: 66px; height: 18.5px;\" width=\"66\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.433px 7.66667px; transform-origin: 127.433px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because 1, 2, 4, 7, 8, 11, 13, and 14 are relatively prime to 15; that is, the greatest common divisor of 15 and each of the eight numbers is 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.525px 7.66667px; transform-origin: 122.525px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn oblique hint is that I call solutions to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sigma(n-1) = phi(n+1)\" style=\"width: 127px; height: 18.5px;\" width=\"127\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.817px 7.66667px; transform-origin: 182.817px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e “Beatriz numbers” in honor of a good friend and former co-worker of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/players/18927291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eEmilyR\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/players/8608872\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eJessicaR\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 268.4px 7.66667px; transform-origin: 268.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The natural search will not help, unless you are interested in combinatorics related to Higham’s conjecture.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.66667px; transform-origin: 3.88333px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Beatriz(m)\r\n  y = f(m);\r\nend","test_suite":"%%\r\nm = 30;\r\ny_correct = [4 6 12 18 30];\r\nassert(isequal(Beatriz(m),y_correct))\r\n\r\n%% \r\nm = 200;\r\ny_correct = [4 6 12 18 30 42 60 72 102 108 138 150 180 192 198];\r\nassert(isequal(Beatriz(m),y_correct))\r\n\r\n%% \r\nm = 1000;\r\ny = Beatriz(m);\r\nhist_correct = [8 7 4 2 3 2 4 0 5 0];\r\ns_correct = 12118;\r\nhist1 = histcounts(y,0:m/10:m);\r\nassert(isequal(hist1,hist_correct) \u0026\u0026 isequal(sum(y),s_correct))\r\n\r\n%% \r\nm = 10000;\r\ny = Beatriz(m);\r\nhist_correct = [35 26 20 22 23 17 19 13 14 16];\r\ns_correct = 863206;\r\nhist1 = histcounts(y,0:m/10:m);\r\nassert(isequal(hist1,hist_correct) \u0026\u0026 isequal(sum(y),s_correct))\r\n\r\n%% \r\nm = 100000;\r\ny = Beatriz(m);\r\nhist_correct = [205 137 125 124 114 106 94 102 109 108];\r\ns_correct = 54557284;\r\nhist1 = histcounts(y,0:m/10:m);\r\nassert(isequal(hist1,hist_correct) \u0026\u0026 isequal(sum(y),s_correct))\r\n\r\n%% \r\nm = 1e6;\r\ny = Beatriz(m);\r\nhist_correct = [1224 936 834 810 761 766 730 705 706 697];\r\ns_correct = 3712183324;\r\nhist1 = histcounts(y,0:m/10:m);\r\nassert(isequal(hist1,hist_correct) \u0026\u0026 isequal(sum(y),s_correct))\r\n\r\n%% \r\nm = 1e7;\r\ny = Beatriz(m);\r\na = y(1:2949:end);\r\na_correct = [4 294180 675840 1093638 1527678 1980660 2458368 2954772 3442122 3941688 4461642 4994790 5535240 6076308 6624972 7185888 7734828 8288340 8852070 9423180];\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\ny = Beatriz(1e9);\r\ns = sum(1./(y-1)+1./(y+1));\r\nB2 = 1.902160583104;\r\ner_correct = 0.127424625465465;\r\nassert(B2-s-er_correct\u003c1e-9)\r\n\r\n%%\r\nfiletext = fileread('Beatriz.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-10T05:12:56.000Z","updated_at":"2025-12-07T06:51:03.000Z","published_at":"2022-01-10T05:18:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e less than or equal to an input value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that solve the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma(n-1) = phi(n+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(n-1) = \\\\phi(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e gives the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46898\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum of divisors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; for example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma(15) = 1+3+5+15 = 24\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(15) = 1+3+5+15 = 24\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/656\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etotient function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phi(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e counts numbers less than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that are relatively prime to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phi(15) = 8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi(15) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e because 1, 2, 4, 7, 8, 11, 13, and 14 are relatively prime to 15; that is, the greatest common divisor of 15 and each of the eight numbers is 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn oblique hint is that I call solutions to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma(n-1) = phi(n+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(n-1) = \\\\phi(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e “Beatriz numbers” in honor of a good friend and former co-worker of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/players/18927291\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eEmilyR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/players/8608872\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJessicaR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The natural search will not help, unless you are interested in combinatorics related to Higham’s conjecture.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54620,"title":"List the Euclid numbers","description":"Euclid proved that the number of primes is infinite with the following argument. Suppose the primes form a finite set , , . Compute . This number  is either prime or composite. \r\nIf it is prime, then the original supposition that the primes form a finite set is false. For example, if we assume that the only primes are 2, 3, and 5, then , which is prime. Therefore, 31 should be in the set of primes. \r\nIf  is composite, then there must be another prime number because  is not divisible by any of the primes in the original set. For example, if we assume the only primes are 2, 3, 5, and 31, then . Therefore, 7 and 19 should be in the set as well. \r\nEither way, a contradiction is reached, and the set of primes must be infinite. In other words, we can always add another prime to the set. \r\nWrite a function to return the th Euclid number  as a character string, where  is the th prime. Take the zeroth Euclid number to be 2. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 269.25px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 134.625px; transform-origin: 407px 134.625px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.75px; text-align: left; transform-origin: 384px 21.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357.85px 7.50833px; transform-origin: 357.85px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEuclid proved that the number of primes is infinite with the following argument. Suppose the primes form a finite set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p_1\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.50833px; transform-origin: 3.88333px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p_2\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.50833px; transform-origin: 3.88333px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p_3,...p_n\" style=\"width: 58px; height: 20px;\" width=\"58\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.225px 7.50833px; transform-origin: 34.225px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"N = p_1 p_2 p_3...p_n + 1\" style=\"width: 127.5px; height: 20px;\" width=\"127.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.725px 7.50833px; transform-origin: 44.725px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. This number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.7917px 7.50833px; transform-origin: 91.7917px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is either prime or composite. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.042px 7.50833px; transform-origin: 378.042px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf it is prime, then the original supposition that the primes form a finite set is false. For example, if we assume that the only primes are 2, 3, and 5, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"N = 31\" style=\"width: 49px; height: 18px;\" width=\"49\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 191.358px 7.50833px; transform-origin: 191.358px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is prime. Therefore, 31 should be in the set of primes. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 7.50833px; transform-origin: 5.825px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 204.208px 7.50833px; transform-origin: 204.208px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is composite, then there must be another prime number because \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.983px 7.50833px; transform-origin: 155.983px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not divisible by any of the primes in the original set. For example, if we assume the only primes are 2, 3, 5, and 31, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"N = 931 = 7^2 19\" style=\"width: 102.5px; height: 19px;\" width=\"102.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 106.967px 7.50833px; transform-origin: 106.967px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, 7 and 19 should be in the set as well. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.883px 7.50833px; transform-origin: 372.883px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEither way, a contradiction is reached, and the set of primes must be infinite. In other words, we can always add another prime to the set. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.75px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.375px; text-align: left; transform-origin: 384px 21.375px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.1px 7.50833px; transform-origin: 90.1px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 54.4583px 7.50833px; transform-origin: 54.4583px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Euclid number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p_1 p_2 p_3...p_n + 1\" style=\"width: 96.5px; height: 20px;\" width=\"96.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.2333px 7.50833px; transform-origin: 90.2333px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as a character string, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 7.50833px; transform-origin: 20.6083px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.5583px 7.50833px; transform-origin: 57.5583px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth prime. Take the zeroth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.9px 7.50833px; transform-origin: 73.9px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Euclid number to be 2. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Euclid(n)\r\n  y = prod(primes(n))+1;\r\nend","test_suite":"%%\r\nn = 0;\r\ny_correct = '2';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct = '7';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 5;\r\ny_correct = '2311';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 13;\r\ny_correct = '304250263527211';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 31;\r\ny_correct = '4014476939333036189094441199026045136645885247731';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = '256041159035492609053110100510385311995538591998443060216114576417920917800321526504084465112487731';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 107;\r\ny_correct = '88943068655955298431534803300631895122870387312920126533061846749648880637254258192829872010273869866014127344907130553732607540259280007645495927216147843286960802658253543903207194796063542641292881808279236107060224463697724254890823931';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 179;\r\ny_correct = '28664469754425230504363571572235469845820264561577835890070872188779971710751376801983001362719551954870499511298235457709201892595062645174236441673457753743915699476691672847636904891194642627609199426015364929706125065438477301579530513319082295731087546945780982302024326869784406913166051214063076904219176752288724404841312943521037527252089602908442634375276528367684811384993103642859137250245700111726555379533421795043360001551344048158371';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 213;\r\ny_correct = '11161858850894038719556889195701685333424794638339968051591498808439960038826329922796050760611433470572584397122296889378549115874800351983437190259473396067677863322943542937282398988783508238390759689612703130677258268615738044560756958767949953020941389380317335519976483204665795427098899445099249099046170398584651763877889367715604803431474006481065495616136755246572134697398757104974146214556304682164605636049604402056819638984183151526317162456055248219001443393537152979493809086912489082711751411396438875436787241895319678096750873200402431';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 257;\r\ny_correct = '351128626489632878379924156757873269334974944630211404005007914024129789363823863845144451044356213600949016525339342409852997414478583477928452879042368781162738403188666797632860335658856799579352360649922899122793124700707033054984240752048623108173938489116606703559378499190646831051963235906799919293537483148239169719906338921711191513814245261193653390937782872494709792008077089488719555947522516094892277236492850263414745518583418722052012316732836495564824531932751371842001101946769787101004438109526486688800220984960665052522225348197933918576328196918309947283657093859600720009196484832286292894803096511656512111814616871885958314637566020331963861179951378504202852863728831';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 311;\r\ny_correct = '83502713393431970802482463921221581691132103739470931177390500537268926567696527894529751704727714035604759199702997383558956931423081803815262105953025919868231628695933266189467051719695967767863336008771178953165902187964483214769691290901572526021482725281429391958818856951536839878153899143852127406725442566530252244959403101788084631518517208058444453478672107472855396563452817908602333022848943488512693549977379932411199960060415810415900332032306927199509145564890515392327495066747931049621955259190755099889574564219516356519410770032523004837173892382410786033114861969336669804939646383513188400988223322875982126007181800865104743107972669462987908190967891479645746726117320867256499622009580740513044927469069016564919644601345042150953497063165749898744098261059073205662877497095246483832632692158726564046225487891467531770064999139236451624634411';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 337;\r\ny_correct = '42854817547059665523332034106437194437255998407058868470591180068473216914846585595991187697905592687127335233314177123580342577449493702868454983939448257533569330527150223502619566844743277023014886761660444588362598446791842424903511976988848622140164498807889085702735069894906702884896068204453339734962942031766546172297446852646437267299209058301580654131798838132093342715780095932012519831850014722152848249980772028337151471363334509749319768370098523366142452279181197268449574953637441392885651873251083229919034973846501968499963746162391501344095645813071800579405863763632457433361231693393116878855988999670350549808695116105212237132127528164581572034266279850325087619570206724200939945340208196601451162516625263365412841271322947309782594274980535126895130479470648931972220532488381341071454561313996042553830515564691370303323574731612496540720911788307065151117866379342369654090822926287013907980830779577436398885716160235886307511';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\nn = 500;\r\ny_correct = '55758984689722289456584343973980218794222360410370486600876521412561125169842671687886659915627578314485846550630950819222944524683009022878904770556027761956176488812292947382221931874253777633437134510302575839253650054921377787870682931197177767075132066757080223218612334159440129580349733289519851712159301522543375931349514587435859733735492107313994296156667043427503419582986673982781662867774668590894039881444170127494445039158987921893949715756676877065894693174740972110652141354362897063044455133797605358546568865726130200450453398931223850324605731252778030970280877206693651731691258544219166428510983029690134652373911775732908004812834312649502260848024341710451795869414983978894963623609913555075593913506181212315124360418666956947337288293197871647777293433519967777021652707770405176662004780202185197896420100824550604276415913952059512150237556052370573695632895271000161855803676535981069482744636004186492414111780359468308325187790134844420749002485723228045872532060620305108426893986989664679237034516531411338218169547038879067681156735284547880657542717850600363029661184202208190403252715716314896654798165882449121636125113013429667194028678491053161776662222026477230231753388170200194252994989570844676016623850478712701514744167948059592159916557939219142408953431605497685148890617736571690321615596678521870072250349196777695604645216560710894365610004262956414917197159252312387646100359038105613845904908753479298728844314517378439149416982869986427478111210565465393664365910491';\r\nassert(strcmp(Euclid(n),y_correct))\r\n\r\n%%\r\npos = [36 112 179 46 22 267 335 21];\r\nn = [72 100 135 166 177 217 264 295];\r\nfor k = randi(8,[1 4])\r\n    assert(isequal(strfind(Euclid(n(k)),'7777'),pos(k)))\r\nend\r\n\r\n%%\r\nfiletext = fileread('Euclid.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, flip('tropmi')) || contains(filetext, 'java') || contains(filetext, 'py') || contains(filetext, 'read'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-05-08T03:58:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-07T14:38:26.000Z","updated_at":"2025-12-14T08:01:55.000Z","published_at":"2022-05-07T14:38:30.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEuclid proved that the number of primes is infinite with the following argument. Suppose the primes form a finite set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p_1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p_2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p_3,...p_n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_3,\\\\ldots,p_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"N = p_1 p_2 p_3...p_n + 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN = p_1p_2p_3{\\\\cdots}p_n + 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. This number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"N\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is either prime or composite. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf it is prime, then the original supposition that the primes form a finite set is false. For example, if we assume that the only primes are 2, 3, and 5, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"N = 31\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN = 31\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, which is prime. Therefore, 31 should be in the set of primes. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is composite, then there must be another prime number because \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"N\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is not divisible by any of the primes in the original set. For example, if we assume the only primes are 2, 3, 5, and 31, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"N = 931 = 7^2 19\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN = 931 = 7^2 19\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, 7 and 19 should be in the set as well. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEither way, a contradiction is reached, and the set of primes must be infinite. In other words, we can always add another prime to the set. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Euclid number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p_1 p_2 p_3...p_n + 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_1p_2p_3{\\\\cdots}p_n + 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as a character string, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth prime. Take the zeroth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Euclid number to be 2. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54755,"title":"List odd twin composites","description":"Twin primes, or prime numbers that differ by 2 (e.g., 17 and 19, 59 and 61, or 191 and 193), are the subject of several Cody problems: 248, 1096, 3016, and 52298. (See also Cody Problem 53740 for “almost twin primes”.)\r\nThis problem deals with twin composites. Because all even numbers are twin composites, let’s focus on odd twin composites, such as 25 and 27, 63 and 65, and 169 and 171. \r\nWrite a function that takes a number and produces a two-column matrix with the smaller number of the odd twin composite pair in the first column and the larger in the second column. \r\nOptional exercises: (a) prove that the number of odd twin composites is infinite, (b) prove that the number of twin primes is infinite. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 195px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.5px; transform-origin: 407px 97.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.775px 8px; transform-origin: 383.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTwin primes, or prime numbers that differ by 2 (e.g., 17 and 19, 59 and 61, or 191 and 193), are the subject of several Cody problems: \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/248\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e248\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1096\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e1096\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/3016\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e3016\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52298\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52298\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. (See also \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53740\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53740\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.95px 8px; transform-origin: 78.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for “almost twin primes”.)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 349.95px 8px; transform-origin: 349.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with twin composites. Because all even numbers are twin composites, let’s focus on odd twin composites, such as 25 and 27, 63 and 65, and 169 and 171. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.667px 8px; transform-origin: 380.667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a number and produces a two-column matrix with the smaller number of the odd twin composite pair in the first column and the larger in the second column. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.617px 8px; transform-origin: 379.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOptional exercises: (a) prove that the number of odd twin composites is infinite, (b) prove that the number of twin primes is infinite. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = twinComposites(n)\r\n  y = ~isprimes(1:2:n);\r\nend","test_suite":"%%\r\nn = 100;\r\ny = twinComposites(n);\r\ny_correct = [25 27; 33 35; 49 51; 55 57; 63 65; 75 77; 85 87; 91 93; 93 95];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1000;\r\ny = twinComposites(n);\r\nlen_correct = 200;\r\nmean_correct = [545.84 547.84];\r\nassert(isequal(length(y),len_correct) \u0026\u0026 isequal(mean(y),mean_correct))\r\n\r\n%%\r\nn = 10000;\r\ny = twinComposites(n);\r\nyi_correct = [121 123; 695 697; 1183 1185; 1659 1661; 2093 2095; 2523 2525; 2979 2981; 3383 3385; 3811 3813; 4213 4215; 4615 4617; 5035 5037; 5433 5435; 5871 5873; 6253 6255; 6655 6657; 7073 7075; 7429 7431; 7855 7857; 8249 8251; 8631 8633; 9051 9053; 9453 9455; 9863 9865];\r\nassert(isequal(y(13:117:2748,:),yi_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = twinComposites(n);\r\nyi_correct = [1387 1389; 6921 6923; 12077 12079; 17161 17163; 22099 22101; 27007 27009; 31807 31809; 36615 36617; 41403 41405; 46161 46163; 50875 50877; 55569 55571; 60357 60359; 64973 64975; 69619 69621; 74303 74305; 78953 78955; 83583 83585; 88157 88159; 92797 92799; 97399 97401];\r\nassert(isequal(y(300:1543:length(y),:),yi_correct))\r\n\r\n%%\r\nn = 1e8;\r\ny = twinComposites(n);\r\nyi_correct = [165453 165455; 5402289 5402291; 10497039 10497041; 15545075 15545077; 20564337 20564339; 25562343 25562345; 30545611 30545613; 35513869 35513871; 40472875 40472877; 45421809 45421811; 50362465 50362467; 55295281 55295283; 60222207 60222209; 65142869 65142871; 70058737 70058739; 74969567 74969569; 79875045 79875047; 84776713 84776715; 89673895 89673897; 94567305 94567307; 99457437 99457439];\r\nassert(isequal(y(54321:1932439:length(y),:),yi_correct))\r\n\r\n%%\r\nn = 2500;\r\ny = twinComposites(n);\r\nz = twinComposites(y(900)^2);\r\na = prod(factor(z(654321,1))+factor(z(654321,2)));\r\na_correct = 17376480;\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nfiletext = fileread('twinComposites.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'read'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-15T03:49:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-15T03:47:54.000Z","updated_at":"2025-09-30T08:35:42.000Z","published_at":"2022-06-15T03:49:28.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwin primes, or prime numbers that differ by 2 (e.g., 17 and 19, 59 and 61, or 191 and 193), are the subject of several Cody problems: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/248\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e248\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1096\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1096\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3016\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3016\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52298\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52298\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (See also \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53740\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53740\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for “almost twin primes”.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with twin composites. Because all even numbers are twin composites, let’s focus on odd twin composites, such as 25 and 27, 63 and 65, and 169 and 171. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a number and produces a two-column matrix with the smaller number of the odd twin composite pair in the first column and the larger in the second column. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOptional exercises: (a) prove that the number of odd twin composites is infinite, (b) prove that the number of twin primes is infinite. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55275,"title":"List the semiprimes","description":"A semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers  and  are semiprimes, but  and  are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems 52859, 52990, and 53740. \r\nWrite a function to list the semiprime numbers less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.167px 8px; transform-origin: 297.167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"6 = 2x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"9 = 3x3\" style=\"width: 60.5px; height: 18px;\" width=\"60.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are semiprimes, but \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"8 = 2x2x2\" style=\"width: 84px; height: 18px;\" width=\"84\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"30 = 2x3x5\" style=\"width: 91.5px; height: 18px;\" width=\"91.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205.517px 8px; transform-origin: 205.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52859\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52859\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52990\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e52990\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53740\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e53740\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.75px 8px; transform-origin: 264.75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = semiprimes(n)\r\n  s = primes(n)/2;\r\nend","test_suite":"%%\r\nn = 100; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 1000; \r\ns = semiprimes(n);\r\ns_correct = [4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95 106 111 115 118 119 121 122 123 129 133 134 141 142 143 145 146 155 158 159 161 166 169 177 178 183 185 187 194 201 202 203 205 206 209 213 214 215 217 218 219 221 226 235 237 247 249 253 254 259 262 265 267 274 278 287 289 291 295 298 299 301 302 303 305 309 314 319 321 323 326 327 329 334 335 339 341 346 355 358 361 362 365 371 377 381 382 386 391 393 394 395 398 403 407 411 413 415 417 422 427 437 445 446 447 451 453 454 458 466 469 471 473 478 481 482 485 489 493 497 501 502 505 511 514 515 517 519 526 527 529 533 535 537 538 542 543 545 551 553 554 559 562 565 566 573 579 581 583 586 589 591 597 611 614 622 623 626 629 633 634 635 649 655 662 667 669 671 674 679 681 685 687 689 694 695 697 698 699 703 706 707 713 717 718 721 723 731 734 737 745 746 749 753 755 758 763 766 767 771 778 779 781 785 789 791 793 794 799 802 803 807 813 815 817 818 831 835 838 841 842 843 849 851 862 865 866 869 871 878 879 886 889 893 895 898 899 901 905 913 914 917 921 922 923 926 933 934 939 943 949 951 955 958 959 961 965 973 974 979 982 985 989 993 995 998];\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nn = 10000; \r\ns = semiprimes(n);\r\nlen_correct = 2625;\r\nsum_correct = 12736914;\r\nvar_correct = 8.447173943104530e+06;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-8)\r\n\r\n%%\r\nn = 100000; \r\ns = semiprimes(n);\r\nlen_correct = 23378;\r\nsum_correct = 1138479765;\r\nvar_correct = 8.471797671132822e+08;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-6)\r\n\r\n%%\r\nn = 800000; \r\ns = semiprimes(n);\r\nlen_correct = 169660;\r\nsum_correct = 66262251604;\r\nvar_correct = 5.417425253731966e+10;\r\nassert(isequal(length(s),len_correct) \u0026\u0026 isequal(sum(s),sum_correct) \u0026\u0026 abs(var(s)-var_correct)\u003c1e-4)\r\n\r\n%%\r\nfiletext = fileread('semiprimes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-08-02T01:42:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-02T01:34:03.000Z","updated_at":"2025-08-03T17:11:25.000Z","published_at":"2022-08-02T01:42:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"6 = 2x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2\\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"9 = 3x3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 3 \\\\times 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are semiprimes, but \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"8 = 2x2x2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2\\\\times2 \\\\times 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"30 = 2x3x5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e30 = 2\\\\times 3 \\\\times 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are not. The semiprimes appear in three of Ramon Villamangca’s “Easy Sequences”: Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52859\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52859\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52990\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e52990\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53740\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e53740\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the semiprime numbers less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57477,"title":"Solve an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there are no solutions, the function should return three empty vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is adapted from one in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.egmo2012.org.uk/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2012 European Girls’ Math Olympiad\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57810,"title":"List the two-bit primes","description":"Each year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the New York Times. This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\r\nIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \r\nRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \r\nWrite a function to list the th two-bit and all its accompanying primes. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 321px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 160.5px; transform-origin: 407px 160.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.108px 8px; transform-origin: 313.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.8417px 8px; transform-origin: 52.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eNew York Times.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1083px 8px; transform-origin: 17.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.058px 8px; transform-origin: 381.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.875px 8px; transform-origin: 379.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80.375px 8px; transform-origin: 80.375px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.808px 8px; transform-origin: 133.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth two-bit and all its accompanying primes. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y,a] = twobitPrime(n)\r\n  y = isprime(n); a = primes(n);\r\nend","test_suite":"%%\r\nn = 1;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 113;\r\na_correct = 311;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 5;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 199;\r\na_correct = 919;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 31;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 977;\r\na_correct = 797;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 311;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 5119;\r\na_correct = 1951;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 500;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 7963;\r\na_correct = [6379 6793];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),sort(a_correct)))\r\n\r\n%%\r\nn = 873;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 13591;\r\na_correct = 59113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 873;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 13591;\r\na_correct = 59113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 1876;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 29009;\r\na_correct = [929 2909];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 5277;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 86069;\r\na_correct = [6869 8669];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 8153;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 134921;\r\na_correct = 492113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 10003;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 168617;\r\na_correct = [861167 861617];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 25000;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 433261;\r\na_correct = [324361 326143 343261];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 39000;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 697877;\r\na_correct = [787697 787769];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\n[y,a] = twobitPrime(twobitPrime(54));\r\ny_correct = 19853;\r\na_correct = [81953 85193];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nfiletext = fileread('twobitPrime.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-19T00:22:09.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-19T00:21:05.000Z","updated_at":"2025-01-02T08:51:14.000Z","published_at":"2023-03-19T00:22:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNew York Times.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth two-bit and all its accompanying primes. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57815,"title":"List numbers such that every sum of consecutive positive integers ending in those numbers is not prime","description":"The sequence in question in this problem involves numbers  such that all sums of consecutive positive integers ending with  are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \r\nWrite a function that returns the th number in this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 46.5px; transform-origin: 469px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 31.5px; text-align: left; transform-origin: 445px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sequence in question in this problem involves numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that all sums of consecutive positive integers ending with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth number in this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = lastInCompositeSum(n)\r\n  y = isprime(sum(n:-1:1));\r\nend","test_suite":"%%\r\nfor n = 1:3:51\r\n    y(ceil(n/3)) = lastInCompositeSum(n);\r\nend\r\ny_correct = [1 18 26 33 39 48 58 63 72 78 85 92 95 104 110 118 123];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 104;\r\ny = lastInCompositeSum(n);\r\ny_correct = 226;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 583;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1028;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1117;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1875;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8513;\r\ny = lastInCompositeSum(n);\r\ny_correct = 12567;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 22698;\r\ny = lastInCompositeSum(n);\r\ny_correct = 32092;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 51734;\r\ny = lastInCompositeSum(n);\r\ny_correct = 71082;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 87777;\r\ny = lastInCompositeSum(n);\r\ny_correct = 118638;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 453867;\r\ny = lastInCompositeSum(n);\r\ny_correct = 588425;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1243598;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1579325;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 890;\r\ny = lastInCompositeSum(lastInCompositeSum(lastInCompositeSum(n)));\r\ny_correct = 3949;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nfiletext = fileread('lastInCompositeSum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2026-03-11T00:52:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-20T03:20:55.000Z","updated_at":"2026-03-11T00:52:46.000Z","published_at":"2023-03-20T03:23:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sequence in question in this problem involves numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that all sums of consecutive positive integers ending with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth number in this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57869,"title":"Identify de Polignac numbers","description":"The numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, , and . The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\r\nWrite a function that determines whether an odd number is a de Polignac number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 297.55px 8px; transform-origin: 297.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMAAAAAmCAYAAACSwZSYAAAG+0lEQVR4Xu2cS+hvUxTH752T14gBxR0QoeQRMbiJUjJQSNK/yGMgySN0kwwQSSZeRTIQysBEeUQReUwMiAGKASMk5nw/Ouu27rn77L3O739e///Zp1a/2//sc/be37W+a6+19j537556VQRWjMDeFc+9Tr0isKcSoBrBqhGoBFi1+uvkKwGqDawagUqAVat/NZN/VzM9UXJae8aVAKuxgdVO9FrN/HXJ95UAq7WB1U78WM38U8mpu40At2lC70t+XK1q68QjCLygRn9J7h2CABjdQ5KrJF8Feqf9luT8pu0/+v1MciD4/K9qd3xHP8nlLDCmJTS5TIN4RPK25LHAgPBi90suadoe1fw+rN83Cs+fq/v3SE5q2p3e6ODlwLOBoU3SBLzullwoOaLp8Qv9Pl2YA889I7lI8rtk4xDIDN+M8Ty9LEcAFPaOxAw/hdJ1hcHT53MZeB/UvYjxTKKhYCdm+IZLZA4Y8IeSvyXe8Rg+OUfwgJ55VOL7QTfgeo0EI7ogOPa5muHBb8l0/qLu3dpx/zv9/U7Je5J/NyEA4N/cvPx6/Rr7SgRg0LSHBC81z5+j3zsk3qPn3oP3/8Q9354jk9opl3lwvPCZEuJRrhIBeO7nBveUw6CyAanA4vIWGDmC8N5vGl28qV+SxCVelrwyP1asPyUnS7Yk3rmmcHxCbVgpjRwbEeAUvcBibF5IHMWVM1zzWLR9PoGqKY1bXeCjvCcl+yWRUGuJyvNjwuC4/pBgsGDAVSIA4Q2e+jfJCYlJgvWXzd8hgDkFTxxwvC/xrK0OJX32wRbHd5akFJpE38mq95ok5eH9+Nv4gAvh5cUSs9+NCOAHGiWAxaRdXgVS/dC8uEuxn+s+7D2sZhtFbsHtogTwOOW8NEbCyuzDGR8+emJ4WDx5hloF0BueuUTsiHqYA+EL8TuOI3X5HHGfM3bG0SbhZAQg7rpRkvPctCEMICk+sjUzbyDcIsb9WAIBd0PFJ0oA7+FyBmVGB1bHNcZiKwd/y63WGAVXSg8RI223GZIAzOEjSSqKsH59fmDzNOJAHn+x6uJwtySEUgftM7oRFl0BIsAZUKkEziu0/S683BWNkiP9LLFNlAAeh5wRe71YnhB91lYPcPIedFPchiRAZAw2dwh8tgQH6fHoeschdjcHAWwFSGXwGMilEkIgyn6WMNpk/GQjIC2tTZQAfnmPEsDifU+ArhAIXKJEiWI4NQFsBYiUxCcLgUpgkaBRk8WQI0kusTClPJJBu7pyh1zf7dCqNM6u+9uNb6MEsPCEcUQJYNUgHxp0JcG7gQDmSG/XZHKhEnNdDAEsQcvVb1PGh+G8JbFSbGTS/j07lQA4CsqnXYmglQqZqxHA/y3nHc2ASiSLOospVwArEkS8/6IIwNLOdUZGqV2AeyNO1b6jipqzXd8VoJSgdmHijTvlLHwVKLoal3CbkgAkyeSDVzfEL42t8/6UOQAJyg2S6FGK1KBtH6FkGBsDMvKDfQlQ8s4+6fNOwfZjbMWk1Gmbkjfp335DLoplJMGMwFfaSC29w6KBrr2m0vOH3J+KAEMN2kKoqNJ6gTFB4ygBouGJN8p2vE++xXERX0ygkkZZ+QOJbchF9wGWQADb5OvaIOutwikIYDtzHAArJSulCZgB7XYC+B3zaBLcJy/yewWlc1klndj9sUMgO9oMgbvO/0THerDd2AQY0vgZtBGgbw6w05JgvxGWM2wfEkaqamDod5mHPBA3JgFGMX7AGJMAEeNnYl0VjhSbrcTXx9t54vT2EK0HpiqDeiPNVcxsvyBaDWE6ZqhDJb9jrwBR4+9rS/+PeywC2KBfbeLQLsPDgz0liZzutPiPHcxNqkjbNf4hno/mAPTV5zBcNIzxu6eDJJEOlLFWAHA4WtI+8er1wYp5jCR18C+rtzEIYMZPx+0zGX4wfOTgP1Q2AO3MRpsUVvriiHbpQ5AhjHWMd/QhQOk4tBEkGg6Oafx+ZdnuKulx9zrnDE/q4uQAEYEdh+iltygB/LZ5ztv4bzAjA/Fg+e1/nkWxrA4w+y4JxyNKB+0ifc7ZxldSIpuBVs5kzF7BVg2LnI8inHpWAvkIlcbCcOgVwCfqJZ1FncBh78kRAOBYUq6UtD9NpHT2taT9VZYv35UG3T7XY8ce2OCw+jWrwS+SVyT02SdfKPU/5X0MHxzbZ5usLPl4Zm6GC+fbwQJHwHeunHknJ+rCBIOn5g+e3zYYbrcKl8NsSAKUvgRrjyMaAvYiwJQGUvsaFgGMkXLhT5Kp/vMA+yAGZzUm0QZFKhoCDdppfVlFYCkIVAIsRRN1HLMgUAkwC+y106UgUAmwFE3UccyCQCXALLDXTpeCQCXAUjRRxzELApUAs8BeO10KApUAS9FEHccsCPwHnjLqNkKdokwAAAAASUVORK5CYII=\" alt=\"125 = 109+2^4\" style=\"width: 96px; height: 19px;\" width=\"96\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"329 = 73+2^8\" style=\"width: 88.5px; height: 19px;\" width=\"88.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 320.392px 8px; transform-origin: 320.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.042px 8px; transform-origin: 255.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isdePolignac(n)\r\n  tf = isequal(n,p+2^k);\r\nend","test_suite":"%%\r\nassert(isdePolignac(1))\r\n\r\n%%\r\nassert(~isdePolignac(17))\r\n\r\n%%\r\nassert(~isdePolignac(75))\r\n\r\n%%\r\nassert(isdePolignac(127))\r\n\r\n%%\r\nassert(isdePolignac(331))\r\n\r\n%%\r\nassert(~isdePolignac(531))\r\n\r\n%%\r\nassert(isdePolignac(905))\r\n\r\n%%\r\nassert(isdePolignac(1619))\r\n\r\n%%\r\nassert(~isdePolignac(2261))\r\n\r\n%%\r\nassert(isdePolignac(7535))\r\n\r\n%%\r\nassert(~isdePolignac(10413))\r\n\r\n%%\r\nassert(isdePolignac(21453))\r\n\r\n%%\r\nassert(isdePolignac(45233))\r\n\r\n%%\r\nassert(~isdePolignac(70999))\r\n\r\n%%\r\nassert(~isdePolignac(96415))\r\n\r\n%%\r\nassert(~isdePolignac(121399))\r\n\r\n%%\r\nassert(isdePolignac(148243))\r\n\r\n%%\r\nassert(isdePolignac(172841))\r\n\r\n%%\r\nassert(isdePolignac(201599))\r\n\r\n%%\r\nassert(isdePolignac(227107))\r\n\r\n%%\r\nassert(isdePolignac(253151))\r\n\r\n%%\r\nassert(~isdePolignac(267267))\r\n\r\n%%\r\nassert(~isdePolignac(271271))\r\n\r\n%%\r\nassert(isdePolignac(273421))\r\n\r\n%%\r\nassert(isdePolignac(542459))\r\n\r\n%%\r\nassert(isdePolignac(2000039))\r\n\r\n%%\r\nassert(~isdePolignac(123456789))\r\n\r\n%%\r\nassert(isdePolignac(123456791))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,5893:2:5933)')'),288))\r\n\r\n%%\r\nassert(isequal(bin2dec(num2str(arrayfun(@isdePolignac,21671:10:21791)')'),4624))\r\n\r\n%%\r\nfiletext = fileread('isdePolignac.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-29T05:27:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-29T05:27:08.000Z","updated_at":"2025-12-25T08:44:06.000Z","published_at":"2023-03-29T05:27:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"125 = 109+2^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125 = 109+2^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"329 = 73+2^8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e329 = 73+2^8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The numbers 127 and 331, which are examples of de Polignac numbers, cannot be written in this way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that determines whether an odd number is a de Polignac number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58018,"title":"List the Fermi-Dirac primes","description":"The Fermi-Dirac “primes” are prime powers with exponents that are powers of 2. The first nine terms of the sequence are 2, 3, 4, 5, 7, 9, 11, 13, and 16. Six of the terms are primes; two are squares of primes; and the remaining term, 16, is . \r\nThe name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes. For example, .\r\nWrite a function analogous to primes(n) that lists the Fermi-Dirac primes less than or equal to .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.892px 8px; transform-origin: 383.892px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Fermi-Dirac “primes” are prime powers with exponents that are powers of 2. The first nine terms of the sequence are 2, 3, 4, 5, 7, 9, 11, 13, and 16. Six of the terms are primes; two are squares of primes; and the remaining term, 16, is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"2^4\" style=\"width: 15.5px; height: 19px;\" width=\"15.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.808px 8px; transform-origin: 373.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"2250 = 2x5x9x25\" style=\"width: 122px; height: 18px;\" width=\"122\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.45px 8px; transform-origin: 92.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function analogous to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.65px 8px; transform-origin: 34.65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eprimes(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167.633px 8px; transform-origin: 167.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that lists the Fermi-Dirac primes less than or equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = FermiDiracPrimes(n)\r\n  y = primes(n).^n;\r\nend","test_suite":"%%\r\nn = 100;\r\ny = FermiDiracPrimes(n);\r\ny_correct = [2 3 4 5 7 9 11 13 16 17 19 23 25 29 31 37 41 43 47 49 53 59 61 67 71 73 79 81 83 89 97];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 500;\r\ny = FermiDiracPrimes(n);\r\ny_correct = [2 3 4 5 7 9 11 13 16 17 19 23 25 29 31 37 41 43 47 49 53 59 61 67 71 73 79 81 83 89 97 101 103 107 109 113 121 127 131 137 139 149 151 157 163 167 169 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 256 257 263 269 271 277 281 283 289 293 307 311 313 317 331 337 347 349 353 359 361 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1000;\r\ny = FermiDiracPrimes(n);\r\nygt500_correct = [503 509 521 523 529 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 625 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 841 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 961 967 971 977 983 991 997];\r\nassert(isequal(y(y\u003e500 \u0026 y\u003c=1000),ygt500_correct))\r\n\r\n%%\r\nn = 100411;\r\ny = FermiDiracPrimes(n);\r\nyselect_correct = [7669 10337 13159 16007 19013 21943 24953 27997 31139 34159 37307 40507 43633 46901 50111 53377 56629 59747 63277 66569 70001 73237 76597 79967 83269 86729 90127 93493 96893 100411];\r\nassert(isequal(y(1001:300:10000),yselect_correct))\r\n\r\n%%\r\nn = 1e6;\r\ny = FermiDiracPrimes(n);\r\ny_correct = [101009 117053 133117 149419 166027 182641 199321 216179 233083 250091 267451 284623 302317 319441 336773 354259 372293 389999 407893 425519 443189 461479 479239 497297 515597 533363 551767 570161 588043 606539 624763 643847 662083 680443 699077 717491 735983 754931 773447 792073 810737 829453 848387 867131 885893 904919 923693 942607 961847 981061];\r\nassert(isequal(y(9750:1379:end),y_correct))\r\n\r\n%%\r\nn = 1e7;\r\ny = FermiDiracPrimes(n);\r\ny_correct = [9999749 9999761 9999823 9999863 9999877 9999883 9999889 9999901 9999907 9999929 9999931 9999937 9999943 9999971 9999973 9999991];\r\nassert(isequal(y(end-15:end),y_correct))\r\n\r\n%%\r\ny1 = FermiDiracPrimes(9035768);\r\ns = sum(FermiDiracPrimes(y1(43560)));\r\ns_correct =  10898621351;\r\nassert(isequal(s,s_correct))\r\n\r\n%%\r\nfiletext = fileread('FermiDiracPrimes.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-25T01:26:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-24T11:56:35.000Z","updated_at":"2024-12-05T13:05:48.000Z","published_at":"2023-04-24T11:56:45.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Fermi-Dirac “primes” are prime powers with exponents that are powers of 2. The first nine terms of the sequence are 2, 3, 4, 5, 7, 9, 11, 13, and 16. Six of the terms are primes; two are squares of primes; and the remaining term, 16, is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2250 = 2x5x9x25\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2250 = 2 \\\\cdot5\\\\cdot9\\\\cdot25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function analogous to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprimes(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that lists the Fermi-Dirac primes less than or equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58019,"title":"Factor a number into Fermi-Dirac primes","description":"Cody Problem 58018 asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, . \r\nWrite a function analogous to factor(n) that factors the number  into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58018\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 58018\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"18\" alt=\"2250 = 2x5x9x25\" style=\"width: 122px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function analogous to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efactor(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that factors the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = factorFD(n)\r\n  y = factor(n).^n;\r\nend","test_suite":"%%\r\nassert(isequal(factorFD(1),1))\r\n\r\n%%\r\np = primes(1000);\r\nfor q = p\r\n    assert(isequal(factorFD(q),q))\r\nend\r\n\r\n%%\r\nassert(isequal(factorFD(56),[2 4 7]))\r\n\r\n%%\r\nassert(isequal(factorFD(64),[4 16]))\r\n\r\n%%\r\nassert(isequal(factorFD(644),[4 7 23]))\r\n\r\n%%\r\nassert(isequal(factorFD(2250),[2 5 9 25]))\r\n\r\n%%\r\nassert(isequal(factorFD(6444),[4 9 179]))\r\n\r\n%%\r\nassert(isequal(factorFD(64444),[4 16111]))\r\n\r\n%%\r\nassert(isequal(factorFD(644444),[4 73 2207]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(5784354),[2 9 211 1523]))\r\n\r\n%%\r\nassert(isequal(factorFD(11739420),[4 5 9 11 49 121]))\r\n\r\n%%\r\nassert(isequal(factorFD(28437991),[17 103 109 149]))\r\n\r\n%%\r\nassert(isequal(factorFD(1106427169),[841 961 1369]))\r\n\r\n%%\r\nassert(isequal(factorFD(753345263125),[13 73 529 625 2401]))\r\n\r\n%%\r\nassert(isequal(factorFD(159360553668481),[14641 83521 130321]))\r\n\r\n%%\r\nassert(isequal(factorFD(2760834326158300),[4 7 25 49 10201 7890481]))\r\n\r\n%%\r\nfiletext = fileread('factorFD.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-28T23:50:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-25T01:29:47.000Z","updated_at":"2025-03-02T18:40:23.000Z","published_at":"2023-04-25T01:29:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58018\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 58018\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2250 = 2x5x9x25\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2250 = 2 \\\\cdot5\\\\cdot9\\\\cdot25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function analogous to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efactor(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that factors the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58498,"title":"Compute the Sisyphus sequence","description":"A recent article in the New York Times featured the Online Encyclopedia of Integer Sequences, founded by Neil J.A. Sloane. One of the sequences discussed in the article is the Sisyphus sequence. The first term is 1. Subsequent terms are computed with this rule: if the previous term is even, then divide it by 2; if the previous term is odd, add the next available prime. Therefore, the sequence starts 1, 3, 6, 3, 8, 4, 2, 1, 8, 4, 2, 1, 12,… \r\nThe sequence gets its name from the story of Sisyphus, whom one of the Greek gods punished by making him roll a boulder up a hill. Every time Sisyphus neared the top, the boulder would roll back down—just as the sequence “rolls” down to 1 when it hits a power of 2. \r\nAn open question is whether every integer appears in this sequence. Some appear multiple times, but others resist appearance for quite a while. For example, 36 appears some time after a billion terms. \r\nWrite a function to generate the Sisyphus sequence and a variant and determine the smallest missing numbers. The function should have two inputs, n and flag, and four outputs, an, z10, amax, and nrestart. The output an is the nth term of the sequence; z10 is a list of the 10 smallest integers not in the sequence; amax is the maximum value in the sequence; and nrestart is the number of times the sequence rolls back to 1 (i.e., not counting the first 1).\r\nIf flag is true or unspecified, generate the sequence as described above—i.e., by adding the next available prime to an odd term. If flag is false, add the next largest unused prime to an odd term. In the latter case, the sequence would start 1, 3, 8, 4, 2, 1, 4, 2, 1, 8, 4, 2, 1, 12, 6, 3, 16, 8, 4, 2, 1… ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 372px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 186px; transform-origin: 407px 186px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA recent \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.nytimes.com/2023/05/21/science/math-puzzles-integer-sequences.html\"\u003e\u003cspan style=\"perspective-origin: 39.675px 8px; transform-origin: 39.675px 8px; \"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003earticle in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 50.9px 8px; transform-origin: 50.9px 8px; \"\u003e\u003cspan style=\"font-style: italic; text-decoration-line: underline; \"\u003eNew York Times\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.225px 8px; transform-origin: 41.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e featured the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eOnline Encyclopedia of Integer Sequences\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.45px 8px; transform-origin: 68.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, founded by Neil J.A. Sloane. One of the sequences discussed in the article is the Sisyphus sequence. The first \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eterm\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 87.5083px 8px; transform-origin: 87.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 1. Subsequent terms are computed with this rule: if the previous term is even, then divide it by 2; if the previous term is odd, add the next available prime. Therefore, the sequence starts 1, 3, 6, 3, 8, 4, 2, 1, 8, 4, 2, 1, 12,… \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.95px 8px; transform-origin: 360.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sequence gets its name from the story of Sisyphus, whom one of the Greek gods punished by making him roll a boulder up a hill. Every time Sisyphus neared the top, the boulder would roll back down—just as the sequence “rolls” down to 1 when it hits a power of 2. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 356.7px 8px; transform-origin: 356.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn open question is whether every integer appears in this sequence. Some appear multiple times, but others resist appearance for quite a while. For example, 36 appears some time after a billion terms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 361.233px 8px; transform-origin: 361.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to generate the Sisyphus sequence and a variant and determine the smallest missing numbers. The function should have two inputs, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 8px; transform-origin: 15.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eflag\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.3333px 8px; transform-origin: 58.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four outputs, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ean\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ez10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 8px; transform-origin: 15.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eamax\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 8px; transform-origin: 30.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003enrestart\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.275px 8px; transform-origin: 39.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The output \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ean\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2167px 8px; transform-origin: 48.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the nth term of the sequence; \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ez10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 173.858px 8px; transform-origin: 173.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a list of the 10 smallest integers not in the sequence; \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 8px; transform-origin: 15.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eamax\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.858px 8px; transform-origin: 124.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the maximum value in the sequence; and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 8px; transform-origin: 30.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003enrestart\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.467px 8px; transform-origin: 250.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of times the sequence rolls back to 1 (i.e., not counting the first 1).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 8px; transform-origin: 15.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eflag\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 362.775px 8px; transform-origin: 362.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is true or unspecified, generate the sequence as described above—i.e., by adding the next available prime to an odd term. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 8px; transform-origin: 15.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eflag\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 343.033px 8px; transform-origin: 343.033px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is false, add the next largest unused prime to an odd term. In the latter case, the sequence would start 1, 3, 8, 4, 2, 1, 4, 2, 1, 8, 4, 2, 1, 12, 6, 3, 16, 8, 4, 2, 1… \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [an,z10,amax,nrestart] = Sisyphus(n,flag)\r\n  an = n+primes(n);\r\n  z10 = find(an~=1:n);\r\n  amax = max(an);\r\n  nrestart = 1;\r\nend","test_suite":"%%\r\nn = 100;\r\nan_correct = 55;\r\nz10_correct = [13 17 19 25 26 27 32 33 34 36];\r\namax_correct = 220;\r\nnrestart_correct = 3;\r\n[an,z10,amax,nrestart] = Sisyphus(n);\r\nassert(isequal(an,an_correct))\r\nassert(isequal(z10,z10_correct))\r\nassert(isequal(amax,amax_correct))\r\nassert(isequal(nrestart,nrestart_correct))\r\n\r\n%%\r\nn = 100;\r\nan_correct = 110;\r\nz10_correct = [13 17 19 25 26 27 32 33 34 36];\r\namax_correct = 220;\r\nnrestart_correct = 4;\r\n[an,z10,amax,nrestart] = Sisyphus(n,false);\r\nassert(isequal(an,an_correct))\r\nassert(isequal(z10,z10_correct))\r\nassert(isequal(amax,amax_correct))\r\nassert(isequal(nrestart,nrestart_correct))\r\n\r\n%%\r\nn = 1000;\r\nan_correct = 990;\r\nz10_correct = [25 27 36 50 54 60 72 75 79 84];\r\namax_correct = 4420;\r\nnrestart_correct = 4;\r\n[an,z10,amax,nrestart] = Sisyphus(n);\r\nassert(isequal(an,an_correct))\r\nassert(isequal(z10,z10_correct))\r\nassert(isequal(amax,amax_correct))\r\nassert(isequal(nrestart,nrestart_correct))\r\n\r\n%%\r\nn = 1000;\r\nan_correct = 1980;\r\nz10_correct = [25 27 36 50 54 60 72 75 79 84];\r\namax_correct = 4420;\r\nnrestart_correct = 5;\r\n[an,z10,amax,nrestart] = Sisyphus(n,false);\r\nassert(isequal(an,an_correct))\r\nassert(isequal(z10,z10_correct))\r\nassert(isequal(amax,amax_correct))\r\nassert(isequal(nrestart,nrestart_correct))\r\n\r\n%%\r\nn = 10000;\r\nan_correct = 24975;\r\nz10_correct = [27 36 54 60 72 79 84 97 107 108];\r\namax_correct = 59820;\r\nnrestart_correct = 4;\r\n[an,z10,amax,nrestart] = Sisyphus(n);\r\nassert(isequal(an,an_correct))\r\nassert(isequal(z10,z10_correct))\r\nassert(isequal(amax,amax_correct))\r\nassert(isequal(nrestart,nrestart_correct))\r\n\r\n%%\r\nn = 10000;\r\nan_correct = 49950;\r\nz10_correct = [27 36 54 60 72 79 84 97 107 108];\r\namax_correct = 59820;\r\nnrestart_correct = 5;\r\n[an,z10,amax,nrestart] = Sisyphus(n,false);\r\nassert(isequal(an,an_correct))\r\nassert(isequal(z10,z10_correct))\r\nassert(isequal(amax,amax_correct))\r\nassert(isequal(nrestart,nrestart_correct))\r\n\r\n%%\r\nn = 1e6;\r\nan_correct = 8820834;\r\nz10_correct = [36 72 97 107 115 127 144 167 194 211];\r\namax_correct = 9466580;\r\nnrestart_correct = 4;\r\n[an,z10,amax,nrestart] = Sisyphus(n);\r\nassert(isequal(an,an_correct))\r\nassert(isequal(z10,z10_correct))\r\nassert(isequal(amax,amax_correct))\r\nassert(isequal(nrestart,nrestart_correct))\r\n\r\n%%\r\nn = 5e6;\r\nan_correct = 8394938;\r\nz10_correct = [36 72 97 107 115 127 144 167 194 211];\r\namax_correct = 53375956;\r\nnrestart_correct = 4;\r\n[an,z10,amax,nrestart] = Sisyphus(n);\r\nassert(isequal(an,an_correct))\r\nassert(isequal(z10,z10_correct))\r\nassert(isequal(amax,amax_correct))\r\nassert(isequal(nrestart,nrestart_correct))\r\n\r\n%%\r\nfiletext = fileread('Sisyphus.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":5,"created_by":46909,"edited_by":46909,"edited_at":"2023-07-19T02:25:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-13T03:32:34.000Z","updated_at":"2024-12-11T00:56:19.000Z","published_at":"2023-07-13T03:32:34.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA recent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.nytimes.com/2023/05/21/science/math-puzzles-integer-sequences.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003earticle in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNew York Times\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e featured the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOnline Encyclopedia of Integer Sequences\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, founded by Neil J.A. Sloane. One of the sequences discussed in the article is the Sisyphus sequence. The first \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eterm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is 1. Subsequent terms are computed with this rule: if the previous term is even, then divide it by 2; if the previous term is odd, add the next available prime. Therefore, the sequence starts 1, 3, 6, 3, 8, 4, 2, 1, 8, 4, 2, 1, 12,… \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sequence gets its name from the story of Sisyphus, whom one of the Greek gods punished by making him roll a boulder up a hill. Every time Sisyphus neared the top, the boulder would roll back down—just as the sequence “rolls” down to 1 when it hits a power of 2. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn open question is whether every integer appears in this sequence. Some appear multiple times, but others resist appearance for quite a while. For example, 36 appears some time after a billion terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to generate the Sisyphus sequence and a variant and determine the smallest missing numbers. The function should have two inputs, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eflag\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four outputs, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ean\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eamax\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enrestart\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The output \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ean\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the nth term of the sequence; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is a list of the 10 smallest integers not in the sequence; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eamax\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the maximum value in the sequence; and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enrestart\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of times the sequence rolls back to 1 (i.e., not counting the first 1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eflag\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is true or unspecified, generate the sequence as described above—i.e., by adding the next available prime to an odd term. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eflag\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is false, add the next largest unused prime to an odd term. In the latter case, the sequence would start 1, 3, 8, 4, 2, 1, 4, 2, 1, 8, 4, 2, 1, 12, 6, 3, 16, 8, 4, 2, 1… \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59126,"title":"Compute the bubble popper fidget spinner sequence","description":"A fidget spinner is a toy made of multiple lobes that pivot on a ball bearing. In some, the lobes hold bubble poppers, or rubber membranes that can be pushed and inverted. Descriptions of such toys say they help the fidgeter concentrate in meetings, classes, and other situations, and some evidence appears to support these claims.  \r\nIn any case, while fidgeting with a bubble popper fidget spinner (BPFS) with five lobes, I thought of using it to create a sequence in this way: Push all of the poppers in. Then number each popper (say blue = 1, green = 2, orange = 3, pink = 4, and yellow = 5). Start by pushing popper 1 out. Then if the “in” position is called 0 and the “out” position is called 1, the poppers on the BPFS give the binary number 00001, or 1 in decimal. \r\nGet the next numbers in the sequence by adding the next prime number to the position of the popper just touched, counting around the BPFS, inverting the popper, and converting the binary number represented by the poppers to decimal. So, for the next number, add the next prime (2) to the current position (1) to get 3, invert popper 3 (0 to 1), and convert 00101 to 5. The next number is 4 because you would add the next prime (3) to the current position (3) to get 6, count around the 5-lobed spinner to position 1, invert the popper from out to in (i.e., 1 to 0), and convert 00100 to 4. \r\nWrite a function to compute the first  terms of the sequence for an -lobed bubble popper fidget spinner. Start each sequence with all poppers except the first in the zero position. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 626.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 313.35px; transform-origin: 407px 313.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.2px 8px; transform-origin: 367.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA fidget spinner is a toy made of multiple lobes that pivot on a ball bearing. In some, the lobes hold bubble poppers, or rubber membranes that can be pushed and inverted. Descriptions of such toys say they help the fidgeter concentrate in meetings, classes, and other situations, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9120292/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esome evidence\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105.017px 8px; transform-origin: 105.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears to support these claims. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365.625px 8px; transform-origin: 365.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn any case, while fidgeting with a bubble popper fidget spinner (BPFS) with five lobes, I thought of using it to create a sequence in this way: Push all of the poppers in. Then number each popper (say blue = 1, green = 2, orange = 3, pink = 4, and yellow = 5). Start by pushing popper 1 out. Then if the “in” position is called 0 and the “out” position is called 1, the poppers on the BPFS give the binary number 00001, or 1 in decimal. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.525px 8px; transform-origin: 383.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGet the next numbers in the sequence by adding the next prime number to the position of the popper just touched, counting around the BPFS, inverting the popper, and converting the binary number represented by the poppers to decimal. So, for the next number, add the next prime (2) to the current position (1) to get 3, invert popper 3 (0 to 1), and convert 00101 to 5. The next number is 4 because you would add the next prime (3) to the current position (3) to get 6, count around the 5-lobed spinner to position 1, invert the popper from out to in (i.e., 1 to 0), and convert 00100 to 4. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.875px 8px; transform-origin: 111.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the first \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.95px 8px; transform-origin: 92.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e terms of the sequence for an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.433px 8px; transform-origin: 147.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-lobed bubble popper fidget spinner. Start each sequence with all poppers except the first in the zero position. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 296.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 148.35px; text-align: left; transform-origin: 384px 148.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"305\" height=\"291\" style=\"vertical-align: baseline;width: 305px;height: 291px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bubblePopperFidgetSpinner(m,n)\r\n  y = mod(cumsum(primes(n)),m);\r\nend","test_suite":"%%\r\nm = 5;\r\nn = 20;\r\ny = bubblePopperFidgetSpinner(m,n);\r\ny_correct = [1 5 4 5 1 9 11 3 7 6 22 23 19 27 25 17 19 18 16 24];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm = 7;\r\nn = 50;\r\ny = bubblePopperFidgetSpinner(m,n);\r\ny_correct = [1 5 37 45 37 36 100 96 97 101 109 45 47 46 44 108 100 36 52 54 50 18 19 83 67 75 11 27 91 83 67 99 107 106 42 40 8 10 2 6 7 23 31 63 59 51 115 114 50 54];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm = 13;\r\nn = 100;\r\ny = bubblePopperFidgetSpinner(m,n);\r\ny_correct = [1 5 37 1061 1077 1073 1077 1141 5237 5749 1653 1637 1633 1649 1905 1913 1897 3945 4073 3561 3565 2541 493 485 487 359 375 383 319 2367 2495 2479 2447 6543 6287 6285 6797 7821 7837 7833 7897 7889 7893 5845 5333 7381 7377 7409 7281 7280 7536 7664 3568 3504 2480 2352 3376 3440 3424 3168 3176 3177 3305 3309 3311 3307 3179 3178 7274 7530 7466 7210 7202 7266 7270 7286 6262 6774 6782 6780 6908 7932 7928 7912 8168 8136 8072 8073 8077 7821 7813 7809 7808 7872 7880 8136 8152 8088 7960 6936];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 200;\r\ny = bubblePopperFidgetSpinner(m,n);\r\nyn_correct = 5;\r\nmaxlen_correct = [11 11];\r\nassert(isequal(y(n),yn_correct))\r\nassert(isequal([sum(y==7),sum(y==19)],maxlen_correct))\r\n\r\n%%\r\nm = 7;\r\nn = 500;\r\ny = bubblePopperFidgetSpinner(m,n);\r\nyn_correct = 75;\r\nmaxlen_correct = [10 10];\r\nassert(isequal(y(n),yn_correct))\r\nassert(isequal([sum(y==2),sum(y==106)],maxlen_correct))\r\n\r\n%%\r\nm = 13;\r\nn = 1000;\r\ny = bubblePopperFidgetSpinner(m,n);\r\nyn_correct = 5838;\r\nmaxlen_correct = [3 3];\r\nassert(isequal(y(n),yn_correct))\r\nassert(isequal([sum(y==7960),sum(y==8136)],maxlen_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 2000;\r\ny = bubblePopperFidgetSpinner(m,n);\r\nd = mean(y)-(2^m-1)/2;\r\nd_correct = 0.315;\r\nassert(abs(d-d_correct)\u003c1e-8)\r\n\r\n%%\r\nm = 7;\r\nn = 5000;\r\ny = bubblePopperFidgetSpinner(m,n);\r\nd = mean(y)-(2^m-1)/2;\r\nd_correct = -0.6098;\r\nassert(abs(d-d_correct)\u003c1e-8)\r\n\r\n%%\r\nm = 13;\r\nn = 10000;\r\ny = bubblePopperFidgetSpinner(m,n);\r\nd = mean(y)-(2^m-1)/2;\r\nd_correct = -21.9005999999;\r\nassert(abs(d-d_correct)\u003c1e-8)\r\n\r\n%%\r\nm = 5;\r\nn = 20000;\r\ny = bubblePopperFidgetSpinner(m,n);\r\nsd_correct = 25;\r\nassert(isequal(setdiff(0:2^m-1,unique(y(end-102:end))),sd_correct))\r\n\r\n%%\r\nm = 7;\r\nn = 50000;\r\ny = bubblePopperFidgetSpinner(m,n);\r\nd = mean(y)-(2^m-1)/2;\r\nsd_correct = 62;\r\nassert(isequal(setdiff(0:2^m-1,unique(y(end-1320:end))),sd_correct))\r\n\r\n%%\r\nfiletext = fileread('bubblePopperFidgetSpinner.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-10-30T03:10:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-29T23:59:40.000Z","updated_at":"2024-12-06T20:30:20.000Z","published_at":"2023-10-29T23:59:40.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA fidget spinner is a toy made of multiple lobes that pivot on a ball bearing. In some, the lobes hold bubble poppers, or rubber membranes that can be pushed and inverted. Descriptions of such toys say they help the fidgeter concentrate in meetings, classes, and other situations, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9120292/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esome evidence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e appears to support these claims. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn any case, while fidgeting with a bubble popper fidget spinner (BPFS) with five lobes, I thought of using it to create a sequence in this way: Push all of the poppers in. Then number each popper (say blue = 1, green = 2, orange = 3, pink = 4, and yellow = 5). Start by pushing popper 1 out. Then if the “in” position is called 0 and the “out” position is called 1, the poppers on the BPFS give the binary number 00001, or 1 in decimal. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGet the next numbers in the sequence by adding the next prime number to the position of the popper just touched, counting around the BPFS, inverting the popper, and converting the binary number represented by the poppers to decimal. So, for the next number, add the next prime (2) to the current position (1) to get 3, invert popper 3 (0 to 1), and convert 00101 to 5. The next number is 4 because you would add the next prime (3) to the current position (3) to get 6, count around the 5-lobed spinner to position 1, invert the popper from out to in (i.e., 1 to 0), and convert 00100 to 4. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the first \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e terms of the sequence for an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-lobed bubble popper fidget spinner. Start each sequence with all poppers except the first in the zero position. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"291\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"305\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59170,"title":"Determine whether a number is a Zeisel number","description":"Do you know what is interesting about the number 1729? \r\nThat’s right: it’s the third Zeisel number, a number given by , where  and  are the distinct prime factors, related by the recurrence relation . For example, A and B are 1 and 6 for 1729 since 1+6 = 7, 7+6 = 13, 13+6 = 19, and .\r\nWrite a function to determine whether a number is a Zeisel number. If it is, return the values of  and . If not, set  and  to NaN.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 73px; transform-origin: 407px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 178.55px 8px; transform-origin: 178.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDo you know what is interesting about the number 1729? \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.317px 8px; transform-origin: 183.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThat’s right: it’s the third Zeisel number, a number given by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJAAAAAoCAYAAAAR33OgAAAGCklEQVR4Xu2aS+htUxzH752T18gEYUDk/SpRFLfkjpTHREZeZWBAGOhmQDGSAW53IOnmETcpxUAi5RlC7uAqJow8ijnfT63f9bvrv9Y+e6+1z+6c+u36dfY5Z6/1e33X77HW3r0rrrBAhwV2d4yNoWGBXQGgAEGXBQJAXeaLwQGgwECXBQJAXeaLwQGgwECXBQJAXeaLwQGgwECXBQJAXeaLwQGgwECXBQJAXeaLwQGgwECXBcYA6CxxOFn0ReLE/WXp/v0u7v8Ptjn9fDemv7/U5x8z8FmCxwxirmWKteleAhCAuUe0V3SOA8odun9edGum4n36/kKD2k9rzIUiA8pvuj9f9IiIOY9zc76u+9s2lEeDWIsMWcK+g4epOOzVpCoOvEb0hIj7k0TfOCdfoXuLUFOsw8r4PQ34TJ8niN4RvSj6U/Su6Mr0/2P6fGrK5OnZJXg0iLXIkLXrPpTC7pWKRBwuosNdIp9icPLdnc4l2h1Jc/yjzyczkHgQw3tPg9mX4NEg1iJD1q77EIBek4qWrm7XPd/9RYh8KP2wX5+kvamXB2lpDtLbe2nSw/o8dyoDPb8Ej5pYLIAHRb+IaikYO14rejtbPDYnUYSFfLrocdGUunPtug8B6G8JSx2C464W5YWsB1BregEcVgOdrfufMk94ALVGoCV4lADkVz//lxaIdzDPlBaqX8g8c0rBFzUAr133GoAul0SfJ6me0efDBQm9cKQWvzKsgPs5ra59+swjGFMaSKl/rirweFS/kda4SnIg53Oib0W1CNjKw1Y+td+pIlIskaBki5IDvQ35v9QIeP14ptSQeDsjw/WisfVmq+4lfYq/1QDkFasVyCacdU8WoT4Vp9NEGJ6IYobMo5Q3cC2CeeN5OaxTtG6tlkJbeQCeT0Qfid4UXSpCRiJyDewlA1udSBS/s+B4+FijwAKk080jPTqQ3o4XHRSNLRVadR8NHh6sAQgQ0P3U0pcPvd759nseLQwIPvz6FFhKXz4F5OmL/+jSaPmpw2oAauXBAjojc5Z3SGvXOck5nQ+36j6JbQ1A/6ZZao6pAexHjWPvKM/lpowHlp+jVBzbmKGwbc+MkXMKDwB/vyivyWr6TTL6Qg/PYd+VopYA5AvXUlFn6a3kWANeXujZnL6TGgKpX+1DG5WrADQHD29Ec8o2RKC5dS+CqQQgv7+TA8EcC3huEeVHD9Zy1wBkadPv7+QgpS74XkThuqq7GwLQXDy84X5NX9gxn+N4ZeUKb3ygR3fKkOtEbBuwsUvkxs4sZK6LfGQuAcjCNA97ICDUAdEPogdEeSfgI9cQgPiPHWXbhPQAAqAvJ8HZPyl1bt6mQwDyC6GHh/Gzmqz16KYRC03DenX3JQcg+lp0cfLZMfrnAPJb33RX34lokTmz+kv01oBTpwCIDodaiUgGIOl2QPyJokMiWt4xK3wIQLYQenmYBwEz8pU6pSYvr3FQr+7W9JBhPhSx4G0/6pgtmxxAvrsq1T9DOvu6ZSgC0RJ/lSZq3cE2OWoA8h1cLw94sTieFd0sygvrNeKgaeo5dLctGt/9FtN3DiC/6zllx9M0HVNE4wg7Y5sK0tyiNQD1LIScBw75WGT7Wk1eXXBQr+6WSXyTZKDccRqQAwiUUby2njtZl1Lambb9GtKAnbG1gNT7ogag3oVgPGyjb+oZ1IJ42cGqV3ezqd85N1DuaGo8gHwKag37qzYSaX8/ENkZW8vh6BgA+XO8Vh62G70v5f+c7xv6YeyRwpKA6tW9tFVhoGTD9wbR0fe/PIB85d7TaSDAeSKKYgphAyagBDz+HaOWl8S8M0xmD/j8PaZWHhSidCCvZN5HL+impN+S4FjFaw7dKUPy4ylACfE+2Jmio+eBAIj8xg90Wv6iM8JBU4tGVi5HDLzRyMthvKrwUmLMvb/o8DhrmvKKAuORmTRo51Pka1LkJaILZuCRn4BnU67cn8qfX+K7vRbSY18DYJ6BrKvbkZnGvBO9hPLBY0stEADaUsdtitgBoE3xxJbKEQDaUsdtitgBoE3xxJbKEQDaUsdtitgBoE3xxJbK8R8qU984j/CwVwAAAABJRU5ErkJggg==\" width=\"72\" height=\"20\" alt=\"p0*p1*p2*...*pn\" style=\"width: 72px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"20\" alt=\"p0 = 1\" style=\"width: 41.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"pk\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.725px 8px; transform-origin: 93.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the distinct prime factors, related by the recurrence relation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"96.5\" height=\"20\" alt=\"pk = Ap(k-1)+b\" style=\"width: 96.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 215.883px 8px; transform-origin: 215.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, A and B are 1 and 6 for 1729 since 1+6 = 7, 7+6 = 13, 13+6 = 19, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"18\" alt=\"1*7*13*19 = 1729\" style=\"width: 129.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 292.35px 8px; transform-origin: 292.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a number is a Zeisel number. If it is, return the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.5917px 8px; transform-origin: 34.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If not, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 8px; transform-origin: 11.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,A,B] = isZeisel(n)\r\n  tf = isunique(factor(n));\r\n  A = NaN;\r\n  B = NaN;\r\nend","test_suite":"%%\r\n[tf,A,B] = isZeisel(1729);\r\nassert(tf \u0026\u0026 isequal(A,1) \u0026\u0026 isequal(B,6))\r\n\r\n%%\r\nassert(all(~arrayfun(@isZeisel,1:104)))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(5719);\r\nassert(tf \u0026\u0026 isequal(A,2) \u0026\u0026 isequal(B,5))\r\n\r\n%%\r\np = primes(20);\r\nassert(~isZeisel(p(randi(8)).^randi(10)))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(27559);\r\nassert(tf \u0026\u0026 isequal(A,4) \u0026\u0026 isequal(B,3))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(233569);\r\nassert(tf \u0026\u0026 isequal(A,9) \u0026\u0026 isequal(B,-2))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(323569);\r\nassert(~tf \u0026\u0026 isnan(A) \u0026\u0026 isnan(B))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(507579);\r\nassert(tf \u0026\u0026 isequal(A,34) \u0026\u0026 isequal(B,-31))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(13725848369);\r\nassert(tf \u0026\u0026 isequal(A,51) \u0026\u0026 isequal(B,-4))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(13725884369);\r\nassert(~tf \u0026\u0026 isnan(A) \u0026\u0026 isnan(B))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(1123229795249);\r\nassert(tf \u0026\u0026 isequal(A,636) \u0026\u0026 isequal(B,-619))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(104177289494129);\r\nassert(tf \u0026\u0026 isequal(A,93) \u0026\u0026 isequal(B,410))\r\n\r\n%%\r\n[tf,A,B] = isZeisel(999965521635409);\r\nassert(tf \u0026\u0026 isequal(A,15831) \u0026\u0026 isequal(B,-15824))\r\n\r\n%%\r\nn = 100*polyval(randi(9,[1 8]),10)+4*randi(24);\r\nassert(~isZeisel(n))\r\n\r\n%%\r\nfiletext = fileread('isZeisel.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp') || contains(filetext,'oeis') || contains(filetext,'read'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2023-11-11T14:45:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-11-11T14:45:15.000Z","updated_at":"2024-12-20T14:17:19.000Z","published_at":"2023-11-11T14:45:28.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDo you know what is interesting about the number 1729? \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThat’s right: it’s the third Zeisel number, a number given by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p0*p1*p2*...*pn\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_0p_1p_2\\\\cdots p_n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p0 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_0 = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"pk\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are the distinct prime factors, related by the recurrence relation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"pk = Ap(k-1)+b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep_k = Ap_{k-1} + B\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, A and B are 1 and 6 for 1729 since 1+6 = 7, 7+6 = 13, 13+6 = 19, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"1*7*13*19 = 1729\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\\\\cdot7\\\\cdot13\\\\cdot19 = 1729\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a number is a Zeisel number. If it is, return the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If not, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59701,"title":"Express numbers as the sum of a prime, a square, and a cube","description":"While traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as , and 17 can be expressed as  or . \r\nWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector [].\r\nOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 228.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 114.25px; transform-origin: 408px 114.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhile traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"144.5\" height=\"19\" alt=\"2+1+8 = 2+1^2+2^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.74167px 8px; transform-origin: 3.74167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and 17 can be expressed as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"144.5\" height=\"19\" alt=\"5+4+8 = 5 + 2^2+2^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 8px; transform-origin: 10.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"144.5\" height=\"19\" alt=\"7+9+1 = 7+3^2+1^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.75px; text-align: left; transform-origin: 385px 52.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.85px 8.5px; transform-origin: 3.85px 8.5px; \"\u003e[\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 341.117px 8px; transform-origin: 341.117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = primeSquareCube(n)\r\n  v = [primes(n) n^2 n^3];\r\nend","test_suite":"%%\r\nn = 11;\r\nv = primeSquareCube(n);\r\nv_correct = [2 1 8];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 17;\r\nv = primeSquareCube(n);\r\nv_correct = [5 4 8; 7 9 1];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 58;\r\nv = primeSquareCube(n);\r\nv_correct = [41 9 8; 41 16 1; 53 4 1];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 82;\r\nv = primeSquareCube(n);\r\nv_correct = [2 16 64; 17 1 64; 17 64 1; 19 36 27; 73 1 8];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 56342;\r\nv = primeSquareCube(n);\r\nsum_correct = [24203820 13786001 8886723];\r\nN_correct = 832;\r\nmax_correct = 56333;\r\nassert(isequal(sum(v),sum_correct))\r\nassert(isequal(size(v,1),N_correct))\r\nassert(isequal(max(v,[],'all'),max_correct))\r\n\r\n%%\r\nn = 4938523;\r\nv = primeSquareCube(n);\r\nsum_correct = [53237782818 28599306108 19254476884];\r\nN_correct = 20470;\r\nmax_correct = 4938473;\r\nassert(isequal(sum(v),sum_correct))\r\nassert(isequal(size(v,1),N_correct))\r\nassert(isequal(max(v,[],'all'),max_correct))\r\n\r\n%%\r\na = NaN(1,10000);\r\nfor n = 1:10000\r\n    v = primeSquareCube(n);\r\n    a(n) = size(v,1);\r\n    if a(n)\u003e0\r\n        assert(all(sum(v,2)==n))\r\n        p = v(:,1); s = v(:,2); c = v(:,3);\r\n        assert(all(isprime(p)))\r\n        assert(all(sqrt(s)==floor(sqrt(s))))\r\n        assert(all(nthroot(c,3)==floor(nthroot(c,3))))\r\n    end\r\nend\r\nu = unique(a);\r\nh = groupcounts(a')';\r\na100_correct = [0 0 0 1 1 0 2 1 1 1 1 3 2 2 3 2 2 1 4 3 2 4 2 3 2 2 2 5 4 3 5 1 5 4 4 5 2 4 6 5 5 3 5 3 4 7 5 6 5 5 3 4 5 6 8 4 6 3 5 6 4 5 6 5 6 4 7 7 6 9 6 5 7 7 7 10 4 9 7 7 8 5 8 10 9 5 8 7 7 6 10 7 8 9 8 10 7 5 9 7];\r\nsum_correct = 1232200;\r\nu_correct = [0:255 258:261 264 273 276];\r\nh_correct = [4 8 11 9 14 19 11 17 16 18 24 25 23 14 28 18 28 29 22 26 25 26 36 26 25 24 31 27 32 37 27 31 31 43 38 32 29 27 31 39 38 23 34 34 47 50 42 38 34 34 37 37 32 38 45 53 39 34 43 45 23 47 32 40 38 54 41 44 38 47 34 49 50 32 53 54 39 43 53 51 45 26 43 52 62 50 59 48 41 45 55 48 41 48 36 48 41 59 57 48 51 48 50 36 53 61 52 55 49 49 46 48 50 52 50 71 55 47 58 53 60 48 52 70 47 51 61 47 67 53 62 63 50 52 52 59 47 55 62 58 59 56 44 49 65 58 54 61 60 58 70 61 58 49 63 55 53 59 54 48 66 53 47 53 56 64 69 51 70 52 65 64 75 53 55 59 56 63 61 53 58 69 61 63 52 48 54 46 49 59 50 61 34 53 38 45 46 33 44 26 31 35 47 40 39 42 31 30 34 27 32 35 35 30 30 23 24 29 21 12 19 26 15 23 20 15 17 12 15 12 8 13 15 9 10 9 13 10 6 6 8 4 5 3 4 3 5 6 7 2 1 4 3 1 2 4 2 1 1 1 1 1 1];\r\nassert(isequal(a(1:100),a100_correct))\r\nassert(isequal(sum(a),sum_correct))\r\nassert(isequal(u,u_correct))\r\nassert(isequal(h,h_correct))\r\n\r\n%%\r\nfiletext = fileread('primeSquareCube.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-16T16:58:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-16T13:48:17.000Z","updated_at":"2025-07-26T04:58:48.000Z","published_at":"2024-03-16T13:51:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhile traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2+1+8 = 2+1^2+2^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2+1+8 = 2+1^2+2^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and 17 can be expressed as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"5+4+8 = 5 + 2^2+2^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5+4+8 = 5 + 2^2+2^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"7+9+1 = 7+3^2+1^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7+9+1 = 7+3^2+1^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59836,"title":"Determine whether a number is a Gaussian prime","description":"A Gaussian prime is a number  that cannot be factored. For example,  is not a Gaussian prime because it can be factored as the product of two Gaussian primes . The number 41 is not a Gaussian prime because it can be factored as , but the number 83 cannot be factored further. \r\nWrite a function to determine whether a number is a Gaussian prime. Just as isprime can handle matrices, your function should handle matrices too. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.075px 8px; transform-origin: 96.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA Gaussian prime is a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"a+bi\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120.175px 8px; transform-origin: 120.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that cannot be factored. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAkCAYAAAAnxQwhAAACxklEQVRoQ+2ZvUscQRjGvV4RtLKyiIU2Egh+QIiFGG20CEI+SP4AI1ikSCApLCw0JKWF+h+o4B+grY0fTQiBpImQJl1sTK/PI/ses3O7M7Pvnse5NwsP3u6+M3vzu+edeXesdcVDRaCmahUbdUVwShNEcBGckoCyWXRcBKckoGymcdwenvUcGofOlc9tRbOfeMhw4IP2EfciJ/YLrr+HUjFFwbHz3eQB7QxuDN/xLBAaw15CNETWcW1cnMPnI54XAfcA8d+g7nsAjhCeQGvQhQPgIe79hwahy5w4ybBfuP9Y4oqAo/V5iP2b7biTpP/X+Pu7gFvs0D5c+ANNQ66pRLLHlabSNx2c6isUHPP8DfQOuqtUlZQo+4NwkDPQhge+OMmVprldhICbResDaDHphfbmUXaA9pdqFrhQs14lgQ81DveBo+1/QJvJL0iIVQAnaXqK8Uw6SHO8jyDCTa26PnCE1Gt0XhVwkqZvMbbtDHA7uDYFyXyeWhgY7wK3hPurEFcnmayrAi4kTc2xNiwgeeBYehxDXM7NX6QK4ELTlMbZStzY4Mw8cCw9vtt5jfMqgPOlqWSuxPG8H0rVeVngWHosQPViz5gDyoBjnTbhmIhDbrFY7QkJdMSEpCmb/4UGIM5vI3Z/NjgpPfKKx/sOLjRNzVe2r4D2wQdO64pm1HStqONC0/QjQK0nsOrvpyY823FVBsea9B/EdPcVvSzDmF2577G+Os52aJlU9U1Nd+04WSV9RS+/J+dBbmZwJ4SOazg6CZy46BMouN5jzflNYrlgfobqK2ungDPT1LdrYs5vQ4D1FHoGvepEcJKmmaWFlYey48vLfGMYheah1FZXpzhO0jSztLDAmRu2nOOWbWiMLwrON8GXuS8bmSvopJ3/l3E7xnYCVwZ6y9tGcErkEVwEpySgbBYdF8EpCSibRcdFcEoCymY3zny1Jc2ewjYAAAAASUVORK5CYII=\" width=\"39\" height=\"18\" alt=\"4+7i\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.467px 8px; transform-origin: 124.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not a Gaussian prime because it can be factored as the product of two Gaussian primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"18.5\" alt=\"(2+i)(3+2i)\" style=\"width: 91px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.808px 8px; transform-origin: 175.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The number 41 is not a Gaussian prime because it can be factored as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"98.5\" height=\"18.5\" alt=\"(5+4i)(5-4i)\" style=\"width: 98.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.233px 8px; transform-origin: 146.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but the number 83 cannot be factored further. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 239.467px 8px; transform-origin: 239.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a number is a Gaussian prime. Just as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.95px 8px; transform-origin: 26.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eisprime\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.467px 8px; transform-origin: 110.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can handle matrices, your function should handle matrices too. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isGaussianPrime(z)\r\n  tf = isprime(complex(z));\r\nend","test_suite":"%%\r\nz = 4+7i;\r\nassert(~isGaussianPrime(z))\r\n\r\n%%\r\nz = 2+i;\r\nassert(isGaussianPrime(z))\r\n\r\n%%\r\nz = 3+2i;\r\nassert(isGaussianPrime(z))\r\n\r\n%%\r\nz = 41;\r\nassert(~isGaussianPrime(z))\r\n\r\n%%\r\nz = 5+4i;\r\nassert(isGaussianPrime(z))\r\n\r\n%%\r\nz = 5-4i;\r\nassert(isGaussianPrime(z))\r\n\r\n%%\r\nz = 83;\r\nassert(isGaussianPrime(z))\r\n\r\n%%\r\nz = 2+3i;\r\nassert(isGaussianPrime(z))\r\n\r\n%%\r\nz = -3-2i;\r\nassert(isGaussianPrime(z))\r\n\r\n%%\r\nz = 1;\r\nassert(~isGaussianPrime(z))\r\n\r\n%%\r\nz = 1i;\r\nassert(~isGaussianPrime(z))\r\n\r\n%%\r\nz = (-1)^randi(40)+(-1)^randi(40)*1i;\r\nassert(isGaussianPrime(z))\r\n\r\n%%\r\nz = primes(30);\r\ntf = isGaussianPrime(z);\r\ntf_correct = [0 1 0 1 1 0 0 1 1 0];\r\nassert(isequal(tf,tf_correct))\r\n\r\n%%\r\np = primes(100);\r\nz = p(p\u003e30)*1i;\r\ntf = isGaussianPrime(z);\r\ntf_correct = [1 0 0 1 1 0 1 0 1 1 0 1 1 0 0];\r\nassert(isequal(tf,tf_correct))\r\n\r\n%%\r\nm = magic(19);\r\nz = m-rot90(m)*1i;\r\ntf = isGaussianPrime(z);\r\nindx = [4 6 17 22 35 38 39 47 77 83 97 101 106 122 135 140 154 155 160 162 178 210 238 243 247 259 277 285 286 311 315 320 324 338 356];\r\ntf_correct = false(19,19);\r\ntf_correct(indx) = true;\r\nassert(isequal(tf,tf_correct))\r\n\r\n%%\r\nz = [37813-37831i -39341+39343i 54990-54991i];\r\ntf = isGaussianPrime(z);\r\ntf_correct = [0 0 1];\r\nassert(isequal(tf,tf_correct))\r\n\r\n%%\r\nz = [-84317-41831i; 52312+17197i; 28184-6334i];\r\ntf = isGaussianPrime(z);\r\ntf_correct = [0; 1; 0];\r\nassert(isequal(tf,tf_correct))\r\n\r\n%%\r\nz = [85765 -  6118i  34368 + 35870i  37281 + 81064i  52415 - 90760i\r\n     61810 + 18400i  44379 - 85972i  -3439 + 64556i   4976 - 32755i\r\n     34761 - 61093i  -7809 + 10291i   2816 - 53793i  51545 + 58168i\r\n     56785 +  9253i  37909 - 28234i  38167 - 16610i  14735 + 39900i];\r\ntf = isGaussianPrime(z);\r\ntf_correct = [0 0 1 0; 0 0 1 0; 0 0 0 1; 0 1 0 0];\r\nassert(isequal(tf,tf_correct))\r\n\r\n%%\r\nfiletext = fileread('isGaussianPrime.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-04-04T02:20:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2024-04-04T02:20:52.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-04T01:34:24.000Z","updated_at":"2025-12-29T17:19:27.000Z","published_at":"2024-04-04T01:34:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Gaussian prime is a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a+bi\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea+bi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that cannot be factored. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"4+7i\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4+7i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is not a Gaussian prime because it can be factored as the product of two Gaussian primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(2+i)(3+2i)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(2+i)(3+2i)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The number 41 is not a Gaussian prime because it can be factored as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(5+4i)(5-4i)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(5+4i)(5-4i)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, but the number 83 cannot be factored further. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a number is a Gaussian prime. Just as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eisprime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e can handle matrices, your function should handle matrices too. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60581,"title":"List primes of the form xy+z","description":"Consider three consecutive integers , , and . When is the number  prime?  For example, if  or , then the results are 17 and 37, both prime, but if  or , the results are 65 and 145, which are composite. \r\nWrite a function to list prime numbers less than or equal to the input that can be written in the form . The function should also return the values of  (i.e., the smallest number of the triple) leading to the primes. \r\nOptional: Prove that the number of primes of this form is infinite. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72px; transform-origin: 407px 72px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.592px 8px; transform-origin: 113.592px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider three consecutive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAAkCAYAAABG3S5jAAADWElEQVR4Xu1aPYxNQRTe7W0IlUqCgmo1fkKjItGJ+ClVfqqNgoRKFCQUCgU2W4nCT7QSslEQCaGg2i2QSIQKBT3fJ3PkuLl7zTszb9+bO+cmX+7NmztzzznfzJlzzrzJCb+qsMBkFVq6khNOdCWTwIl2oiuxQCVq+op2oiuxQCVq+ooum+gNEP8isArY26WKE10m0ULwoSD+Yye6TCK7pD6Lxi1hFe9xokdP8AmIcBR4CpzJKA5X8/sw3i8nOqNljUNdRr/TwH/dqnF8dnOiE4yXq6sTncuSYz5OEURzkz8ATAMrgU3AEeBuw7gLoW0W9+NjbniKx/2NkepuYCewAtio9ryteL4GbAfuAYcTdCqCaNGPhD8IBlnEffMSRPPnNcC3CMO8CIaMeHXJV36iZcowAAOkD8B64HroL4SS5CfAJ4ATm/ruitSpTZSiiKYCIjCftwGvlFar8fwQ4KqPNcooidaEiDcSQp+j8TxAr0XSOWklujXMqb92KyYYo7t7FzS9gnszVeBEWAekuDmLIVP73MQAx8IgJONti24p3yhuRVNZmf0v8byjoT3bZgAaq6SLE/NOEJh67QurOFYHbmuPYl/ueO8c2i4Zx8meXmn3rYMXKnvBYCSjXlm7cdv5Gka0BJO9JForpaNv7rdXgWY0npWRIQ72GWOvDd6o81DAIEORrpt6ipuQ2W9dzeMSjGkvRf1yH/AUS7QQJGkWV8Mpw2oeB6IlbeQRH8GLKzpnnFEs0SI4c1jmoCym5HZ3Bg85cBfuzR8BFoReq31aZxQ8IbIGSCJQsUTrfZpk86gsJc8cmKGEDpSdsn4HmC/fUkQ2MwrGG5wIqSdOxRKto9SUlCCBL1NXrk5xz5ygLPCcBKSKp/PpL/j9WaPd9FF0GjbReuG1VS3/kXvQAIQBmSXntBorRz/my3MA69oMJEm8LtWyIERyGX23tVtlGBbRLOPuB+RPByIfJ+lt4D6gq5d/2gchmgZ5A5Tksq0k5egnfzxgxW3kBz6xRNNt61pwDkP4GMtogViicwUoy6iaf0pboI1ontwcBOYB5pVS9dIBjFuxMAu0Ea0LGjmj0MJM0y9x24hmEMHiwQ+ABxY3+qVyndrE7tF1WqdHWjvRPSKzSxUnuhKifwMnyc8l2WbS3AAAAABJRU5ErkJggg==\" width=\"61\" height=\"18\" alt=\"y = x+1\" style=\"width: 61px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59.5\" height=\"18\" alt=\"z = x+2\" style=\"width: 59.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.45px 8px; transform-origin: 68.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. When is the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" alt=\"xy+z\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e prime? \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.225px 8px; transform-origin: 48.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 3\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.45833px 8px; transform-origin: 1.45833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 5\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 154.792px 8px; transform-origin: 154.792px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then the results are 17 and 37, both prime, but if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 7\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 8px; transform-origin: 10.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" alt=\"x = 11\" style=\"width: 44px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120.967px 8px; transform-origin: 120.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the results are 65 and 145, which are composite. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 305.192px 8px; transform-origin: 305.192px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list prime numbers less than or equal to the input that can be written in the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should also return the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.192px 8px; transform-origin: 190.192px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., the smallest number of the triple) leading to the primes. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.517px 8px; transform-origin: 199.517px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOptional: Prove that the number of primes of this form is infinite. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,x] = xyzPrimes(n)\r\n  p = primes(n);\r\n  x = (p-2)./p;\r\nend","test_suite":"%%\r\nn = 100;\r\n[p,x] = xyzPrimes(n);\r\np_correct = [2 5 17 37];\r\nx_correct = [0 1 3 5];\r\nassert(isequal(p,p_correct))\r\nassert(isequal(x,x_correct))\r\n\r\n%%\r\nn = 1000;\r\n[p,x] = xyzPrimes(n);\r\np_correct = [2 5 17 37 101 197 257 401 577 677];\r\nx_correct = [0 1 3 5 9 13 15 19 23 25];\r\nassert(isequal(p,p_correct))\r\nassert(isequal(x,x_correct))\r\n\r\n%%\r\nn = 100000;\r\n[p,x] = xyzPrimes(n);\r\np_correct = [2 5 17 37 101 197 257 401 577 677 1297 1601 2917 3137 4357 5477 7057 8101 8837 12101 13457 14401 15377 15877 16901 17957 21317 22501 24337 25601 28901 30977 32401 33857 41617 42437 44101 50177 52901 55697 57601 62501 65537 67601 69697 72901 78401 80657 90001 93637 98597];\r\nx_correct = [0 1 3 5 9 13 15 19 23 25 35 39 53 55 65 73 83 89 93 109 115 119 123 125 129 133 145 149 155 159 169 175 179 183 203 205 209 223 229 235 239 249 255 259 263 269 279 283 299 305 313];\r\nassert(isequal(p,p_correct))\r\nassert(isequal(x,x_correct))\r\n\r\n%%\r\nn = 1e7;\r\n[p,x] = xyzPrimes(n);\r\npsum_correct = 978608577;\r\nxsum_correct = 467675;\r\nassert(isequal(sum(p),psum_correct))\r\nassert(isequal(sum(x),xsum_correct))\r\n\r\n%%\r\nn = 3e10;\r\n[p,x] = xyzPrimes(n);\r\nlen_correct = 10840;\r\npsum_correct = 100249886422757;\r\nxsum_correct = 883807319;\r\nassert(isequal(length(p),len_correct))\r\nassert(isequal(sum(p),psum_correct))\r\nassert(isequal(sum(x),xsum_correct))\r\nassert(isequal(p(10500:10502),[28009369601 28031465477 28036153601]))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-07-04T21:58:30.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-07-04T21:58:04.000Z","updated_at":"2025-07-26T18:47:04.000Z","published_at":"2024-07-04T21:58:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider three consecutive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = x+1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = x + 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"z = x+2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez = x+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. When is the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xy+z\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exy+z\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e prime? \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then the results are 17 and 37, both prime, but if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 7\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the results are 65 and 145, which are composite. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list prime numbers less than or equal to the input that can be written in the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003exy+z\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should also return the values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., the smallest number of the triple) leading to the primes. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOptional: Prove that the number of primes of this form is infinite. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}