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An n-step Lucas sequence {L_k^((n))}_(k=1)^infty is defined by letting L_k^((n))=-1 for k<0, L_0^((n))=n, and other terms according to the linear recurrence equation ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

A set of m distinct positive integers S={a_1,...,a_m} satisfies the Diophantus property D(n) of order n (a positive integer) if, for all i,j=1, ..., m with i!=j, ...

Kobon Fujimura asked for the largest number N(n) of nonoverlapping triangles that can be constructed using n lines (Gardner 1983, p. 170). A Kobon triangle is therefore ...

Landau's function g(n) is the maximum order of an element in the symmetric group S_n. The value g(n) is given by the largest least common multiple of all partitions of the ...

Rule 110 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Rule 90 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

The (small) rhombicosidodecahedron (Cundy and Rowlett 1989, p. 111), sometimes simply called the rhombicosidodecahedron (Maeder 1997; Wenninger 1989, p. 27; Conway et al. ...

A number v=xy with an even number n of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...