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The self-describing sequence consisting of "blocks" of single and double 1s and 2s, where a "block" is a single digit or pair of digits that is different from the digit (or ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...

Given a hereditary representation of a number n in base b, let B[b](n) be the nonnegative integer which results if we syntactically replace each b by b+1 (i.e., B[b] is a ...

The sequence of numbers {j_n} giving the number of digits in the three-fold power tower n^(n^n). The values of n^(n^n) for n=1, 2, ... are 1, 16, 7625597484987, ... (OEIS ...

Define the juggler sequence for a positive integer a_1=n as the sequence of numbers produced by the iteration a_(k+1)={|_a_k^(1/2)_| for even a_k; |_a_k^(3/2)_| for odd a_k, ...

Let P, Q be integers satisfying D=P^2-4Q>0. (1) Then roots of x^2-Px+Q=0 (2) are a = 1/2(P+sqrt(D)) (3) b = 1/2(P-sqrt(D)), (4) so a+b = P (5) ab = 1/4(P^2-D) (6) = Q (7) a-b ...

The Ulam sequence {a_i}=(u,v) is defined by a_1=u, a_2=v, with the general term a_n for n>2 given by the least integer expressible uniquely as the sum of two distinct earlier ...

A sequence produced by the instructions "reverse, add to the original, then sort the digits." For example, after 668, the next iteration is given by 668+866=1534, so the next ...

The Beatty sequence is a spectrum sequence with an irrational base. In other words, the Beatty sequence corresponding to an irrational number theta is given by |_theta_|, ...