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Stirling Numbers - I
Problems #1388 & #45187 deal with Stirling numbers of the 2nd Kind. Here, generate the Stirling numbers S(n,k) of the 1st kind ...

10 mesi fa

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Total Area Covered by Overlapping Polygons
Given a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with t...

10 mesi fa

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Determine if LTI system with feedback control is stable
Linear timeiinvariant systems can be represented by the differential equation , where is an matrix, is an vector representing...

10 mesi fa

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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)...

10 mesi fa

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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...

10 mesi fa

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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...

10 mesi fa

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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 - ...

10 mesi fa

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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...

10 mesi fa

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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] ...

10 mesi fa

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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...

10 mesi fa

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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 ...

11 mesi fa

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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...

12 mesi fa

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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,...

12 mesi fa

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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...

12 mesi fa

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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...

12 mesi fa

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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...

12 mesi fa

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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...

12 mesi fa

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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...

12 mesi fa

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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,...

12 mesi fa

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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...

12 mesi fa

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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 ...

12 mesi fa

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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...

12 mesi fa

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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 ...

12 mesi fa

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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...

12 mesi fa

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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 : ...

12 mesi fa

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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 ...

12 mesi fa

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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...

12 mesi fa

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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...

12 mesi fa

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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...

12 mesi fa

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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...

12 mesi fa