Problem 2369. Tribute to Ramanujan

Created by rifat

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The nth taxicab number, denoted as T(n), is defined as the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways (source: wikipedia).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[           T(1) = 2 = 1^3 + 1^3\n           T(2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Return the value of n if the given number is a taxicab number. Return 0 if not. If the input is 1729, output would be 2, since 1729 is smallest number that can be expressed as a sum of two cubes in two (n=2) distinct ways.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Avoid look up table solution. Test suit might expand.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

45 Solutions
24 Solvers

Last Solution submitted on Sep 10, 2022

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Rafael S.T. Vieira on 13 Oct 2020

The solution must be a lookup table since the 6th taxicab number is already greater than 2^64. If anyone find an algorithm for this, DO NOT publish here, publish a scientific paper. Researchers published a paper just about the upper bounds for the 7th to12th number for instance.

Rafael S.T. Vieira on 13 Oct 2020

The 6th taxicab number is not even a certainty apparently http://jucs.org/jucs_9_10/what_is_the_value/Calude_C_S.pdf

GeeTwo on 10 Sep 2022 at 22:04

Still, there's a lot that can be done to show that this might be a general solution within MATLAB numeric bounds.
Test cases! E.g. 9 and 4104 would catch when someone isn't checking that they have the SMALLEST number for a given number of ways. (e.g. 9==2^3+1^3, and 4104 == 16^3 + 2^3 == 15^3 + 9^3 are the SECOND smallest numbers for 1 and 2 ways. Random cases could be defined for this one).
Outlaw shortcut functions like str2num. Outlaw the string "1729" and other ways to calculate it and other known taxicab numbers as other than the sum of two cubes two ways. [e.g. it turns out that 1729==prod(1:6:19)].

Solution Comments

Solution 457767

3 Comments

3 Comments

rifat on 18 Jun 2014

not a general solution

Guillaume on 19 Jun 2014

Considering that the proof of the 6th taxicab number produced over 8GB of data and consisted of an exhaustive search over the integers up to 1e21, a truly generic solution is not really possible.

Jean-Marie Sainthillier on 20 Jul 2014

:-)

Problem Recent Solvers24

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 2369. Tribute to Ramanujan

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers24

Suggested Problems

More from this Author44

Problem Tags

Community Treasure Hunt

Problem 2369. Tribute to Ramanujan

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers24

Suggested Problems

More from this Author44

Problem Tags

Community Treasure Hunt

Players