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An infinite sequence of positive integers 1<=b_1<b_2<b_3<..., (1) also called a Sidon sequence, such that all pairwise sums b_i+b_j (2) for i<=j are distinct (Guy 1994). An ...

Consider the sequence defined by w_1=01 and w_(n+1)=w_nw_nw_n^R, where l^R denotes the reverse of a sequence l. The first few terms are then 01, 010110, 010110010110011010, ...

Wolfram (2002, p. 123) considered the sequence related to the Collatz problem obtained by iterating w_n={3/2w_(n-1) for w_(n-1) even; 3/2(w_(n-1)+1) for w_(n-1) odd (1) ...

An Achilles number is a positive integer that is powerful (in the sense that each prime factor occurs with exponent greater than one) but imperfect (in the sense that the ...

The largest cube dividing a positive integer n. For n=1, 2, ..., the first few are 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, ... (OEIS A008834).

An exponential generating function for the integer sequence a_0, a_1, ... is a function E(x) such that E(x) = sum_(k=0)^(infty)a_k(x^k)/(k!) (1) = ...

An even number of the form 4n+2 (i.e., an integer which is divisible by 2 but not by 4). The first few for n=0, 1, 2, ... are 2, 6, 10, 14, 18, ... (OEIS A016825)

A function composed of a set of equally spaced jumps of equal length, such as the ceiling function f(x)=[x], floor function f(x)=|_x_|, or nearest integer function f(x)=[x].

An interspersion array given by 1 2 3 5 8 13 21 34 55 ...; 4 6 10 16 26 42 68 110 178 ...; 7 11 18 29 47 76 123 199 322 ...; 9 15 24 39 63 102 165 267 432 ...; 12 19 31 50 81 ...

For a discrete function f(n), the summatory function is defined by F(n)=sum_(k in D)^nf(k), where D is the domain of the function.