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Moyenne pondérée
Ecrire une fonction qui prend en entrée un vecteur P et un vecteur V et calcule la moyenne pondérée MP des élements vi d'un vec...

2 years ago

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Easy Sequences 6: Coefficient sums of derivatives
Consider the polynomial function and its first-order derivative . The sums of the coefficients of P and P', are and , respecti...

2 years ago

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Easy Sequences 5: Project Euler Problem 1 - Again!
We are all familiar with Project Euler Problem 1. This time let's try it on bigger multiples and larger range. Find the sum of ...

2 years ago

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Easy Sequences 4: Eliminate the Days of Confusion
If a date is written in purely numeric format some dates can be confusing, if we don't know the date format used. For example, "...

2 years ago

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Easy Sequences 3: Prime 44-number Squares
The positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd ...

2 years ago

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Easy Sequences 2: Trigonometric function with integral input and output
The function 'F', defined as: , will always return an integer if the input is a natural number (in radian...

2 years ago

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Explore the twin prime Goldbach conjecture
The Goldbach conjecture says that every positive even integer greater than 2 can be expressed as the sum of two prime numbers in...

2 years ago

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Hermite Polynomials
Return the _n_-th <http://en.wikipedia.org/wiki/Hermite_polynomials Hermite polynomial> of the physicists' type. Assume that ...

2 years ago

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Damping of Servomotors with Tachometer Feedback
In Control Engineering, servomotors with tachometer feedback can be modeled by the second order system K / [J*s^2 + (B + K*K...

2 years ago

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Express numbers as the sum of a prime, a square, and a cube
While traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 m...

2 years ago

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Determine whether a number is a Gaussian prime
A Gaussian prime is a number that cannot be factored. For example, is not a Gaussian prime because it can be factored as the p...

2 years ago

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Determine whether a number is a Zeisel number
Do you know what is interesting about the number 1729? That’s right: it’s the third Zeisel number, a number given by , where ...

2 years ago

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Compute the bubble popper fidget spinner sequence
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...

2 years ago

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Compute the Sisyphus sequence
A recent article in the New York Times featured the Online Encyclopedia of Integer Sequences, founded by Neil J.A. Sloane. One o...

2 years ago

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Factor a number into Fermi-Dirac primes
Cody Problem 58018 asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As note...

2 years ago

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List the Fermi-Dirac primes
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,...

2 years ago

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List numbers such that every sum of consecutive positive integers ending in those numbers is composite
The sequence in question in this problem involves numbers such that all sums of consecutive positive integers ending with are ...

2 years ago

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Identify de Polignac numbers
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, whi...

2 years ago

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List the two-bit primes
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 e...

2 years ago

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Solve an equation involving primes and fractions
Write a function to find pairs of primes and satisfying the equation where is an integer. The function should take a numbe...

2 years ago

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List the semiprimes
A semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers and are semiprimes, but and are not....

2 years ago

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List odd twin composites
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 pro...

2 years ago

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List the Euclid numbers
Euclid proved that the number of primes is infinite with the following argument. Suppose the primes form a finite set , , . Comp...

2 years ago

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List the Beatriz numbers
Write a function to find integers less than or equal to an input value that solve the equation . The function gives the sum o...

2 years ago

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Compute the largest number whose prime factors sum to n
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 ...

2 years ago

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List the Moran numbers
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 ...

2 years ago

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Solve the arithmetic differential equation D(n) = n

2 years ago

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Compute the arithmetic derivative of integers

2 years ago

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List composite numbers that cannot be written as the sum of two primes

2 years ago

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Find pairs of primes with the same digit sum and a specified separation

2 years ago