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A sequence {x_n} is called an infinitive sequence if, for every i, x_n=i for infinitely many n. Write a(i,j) for the jth index n for which x_n=i. Then as i and j range ...

A sequence defined from a finite sequence a_0, a_1, ..., a_n by defining a_(n+1)=max_(i)(a_i+a_(n-i)).

A Meeussen sequence is an increasing sequence of positive integers (m_1, m_2, ...) such that m_1=1, every nonnegative integer is the sum of a subset of the {m_i}, and each ...

If a_1, a_2, a_3, ... is an artistic sequence, then 1/a_1, 1/a_2, 1/a_3, ... is a melodic sequence. The recurrence relation obeyed by melodic series is ...

A sequence defined from a finite sequence a_0, a_1, ..., a_n by defining a_(n+1)=mex_(i)(a_i+a_(n-i)), where mex is the mex (minimum excluded value).

A spectrum sequence is a sequence formed by successive multiples of a real number a rounded down to the nearest integer s_n=|_na_|. If a is irrational, the spectrum is called ...

A tournament sequence is an increasing sequence of positive integers (t_1, t_2, ...) such that t_1=1 and t_(i+1)<=2t_i. Cook and Kleber (2000) show that Meeussen sequences ...

A recursive sequence {f(n)}_n, also known as a recurrence sequence, is a sequence of numbers f(n) indexed by an integer n and generated by solving a recurrence equation. The ...

A graphic sequence is a sequence of numbers which can be the degree sequence of some graph. A sequence can be checked to determine if it is graphic using GraphicQ[g] in the ...

An infinite sequence of positive integers a_i satisfying 1<=a_1<a_2<a_3<... (1) is an A-sequence if no a_k is the sum of two or more distinct earlier terms (Guy 1994). Such ...