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Bernstein Basis Polynomials
Return the coefficients of a Bernstein Basis Polynomial B(v,n) for degree n and order v - %Examples B(2, 5) = 10*x^2*(1-x)...

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Multiply real numbers to get the smallest integers
Write a function that takes a vector of real numbers and multiplies them by a factor to produce the integers with the smallest a...

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Dickson Polynomials
Return the coefficients of nth (n>=0) Dickson polynomial of the 1st kind as follows - 1st row of the output will be the coeffi...

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Cummulative Count
Given a row vector of integers (with repeating values) , create an array that is the cumulative count of the unique values - ...

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Search for seesaw primes
Cody Problem 60958 introduced seesaw numbers. A number is a seesaw number if the next smaller numbers can be placed on a seesa...

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find powers of two
find the unique, non-repeating, powers of 2 that sum to a given non-zero integer, n example: n = 23 result = [1 2 4 16] ...

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Grimm's Conjecture
Grimm's conjecture states that to each element of a set of consecutive composite numbers, one can assign a unique prime number t...

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Find the Prime Factors and Divisors of a Number
Given a positive integer n, find its prime factors as well as all of its divisors. Example: n=12 has prime factors [2,2,3] and ...

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List numbers that cannot be expressed as the sum of two primes
The Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the...

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Mesh the convex hull of a random 3D point cloud
Problem statement The convex hull of a 3D point set is actually a first -though rough- triangulation of it. A triangulation,...

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Mesh the icosahedron
Problem statement An icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five...

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Mesh the dodecahedron
Problem statement An dodecahedron is a regular polyhedron with 20 vertices and 12 pentagonal faces. It is also one of the fiv...

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Build triangulation from -sorted- edge list
Problem statement An edge list is simply a N x 2 matrix of positive integers, in which N is the number of edges and each intege...

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Check Euler's characteristic on regular polyhedra
Problem statement Given the number of vertices and the number of faces of a given regular polyhedron, compute the number of its...

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Mesh the square with triangles
Problem statement An square is a regular polygon with 4 vertices and 4 edges. Here below is an example of the vertex set V, c...

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Mesh the pentagon (with the minimum number of triangles)
Problem statement An pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V,...

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Mesh the tetrahedron
Problem statement An tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five w...

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Mesh the cube
Problem statement : mesh the cube with quadranglar / squared faces An cube / regular hexahedron is a regular polyhedron with ...

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Mesh the octahedron
Problem statement An octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five we...

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Monkey and the Peaches
A monkey picked a certain number of peaches on the first day. Each day, the monkey eats half of the remaining peaches plus one ...

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Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...

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Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...

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Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...

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List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...

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Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...

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List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...

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Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...

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List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...

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Easy Sequences 113: Almost Golden Integer Rectangles 2
A golden rectangle is a rectangle whose side lengths are in the golden ratio, , where: . ...

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List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...

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