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Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n)=n,s^1(n)=s(n),s^2(n)=s(s(n)),... ...

The sequence defined by G(0)=0 and G(n)=n-G(G(n-1)). (1) The first few terms for n=1, 2, ... are 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, ... (OEIS A005206). This can be ...

A generalization of the Fibonacci numbers defined by the four constants (p,q,r,s) and the definitions H_0=p and H_1=q together with the linear recurrence equation ...

An integer sequence whose terms are defined in terms of number-related words in some language. For example, the following table gives the sequences of numbers having digits ...

A generalization of an Ulam sequence in which each term is the sum of two earlier terms in exactly s ways. (s,t)-additive sequences are a further generalization in which each ...

Consider the recurrence relation x_n=(1+x_0^2+x_1^2+...+x_(n-1)^2)/n, (1) with x_0=1. The first few iterates of x_n are 1, 2, 3, 5, 10, 28, 154, ... (OEIS A003504). The terms ...

A sequence of positive integers 1<=a_1<a_2<a_3<... (1) is a nonaveraging sequence if it contains no three terms which are in an arithmetic progression, i.e., terms such that ...

A sequence which arises in the hypothetical reproduction of a population of rabbits. Let the substitution system map 0->1 correspond to young rabbits growing old, and 1->10 ...

The score sequence of a tournament is a monotonic nondecreasing sequence of the outdegrees of the graph vertices of the corresponding tournament graph. Elements of a score ...

A sequence a_1, a_2, ... such that the metric d(a_m,a_n) satisfies lim_(min(m,n)->infty)d(a_m,a_n)=0. Cauchy sequences in the rationals do not necessarily converge, but they ...