Sequences

Successive digits of even numbers.

When the 'Summarize preceding term' sequence gets into a cycle.

Duplicating binary multipliers; i.e., n+1 1-bits placed 2n bits from each other.

Bit-reversing masks for 2*n bits.

Binary reversal of 3^n.

Expansion of 1/(1 - 3*x)^4; 4-fold convolution of A000244 (powers of 3).

Expansion of 1/(1-3*x)^5; 5-fold convolution of A000244 (powers of 3).

Hours recorded by a 24-hour clock.

Expansion of 1/(1-3*x)^6; 6-fold convolution of A000244 (powers of 3).

Expansion of 1/(1-3*x)^7; 7-fold convolution of A000244 (powers of 3).

Expansion of 1/(1-3*x)^8; 8-fold convolution of A000244 (powers of 3).

Expansion of 1/(1-3*x)^9; 9-fold convolution of A000244 (powers of 3).

Expansion of 1/(1-3*x)^10; 10-fold convolution of A000244 (powers of 3).

Expansion of (-1+1/(1-6*x)^6)/(36*x); related to A036084.

Length of cycle the 'summarize the previous term' sequence gets into.

Expansion of 1/(1-7*x)^7.

a(1) = 20; a(n+1) = a(n) + sum of decimal digits of a(n).

a(1) = 31; a(n+1) = a(n) + sum of decimal digits of a(n).

Smallest n-digit prime containing only digits 1 or 2 or -1 if no such prime exists.

a(n+1) = a(n) + sum of digits of a(n) starting with 110.

a(n+1) = a(n) + sum of digits of a(n) starting with 121.

a(n+1) = a(n) + sum of digits of a(n) starting with 211.

Inverse Colombian function.

Number of primes <= n, if 1 is counted as a prime.

Found on a quiz long ago.

Least inverse of A015910: smallest integer k > 0 such that 2^k mod k = n, or 0 if no such k exists.

Duplicate of A015948.

Triangle of numbers a(r,j) = j*(j+1) mod r+2, r>=1, j=1..r.

Number of 2-element intersecting families of an n-element set; number of 2-way interactions when 2 subsets of power set on {1..n} are chosen at random.

Number of 3-way interactions when 3 subsets of power set on {1..n} are chosen at random; number of Boolean functions of n variables and rank 3 from Post class F(8,inf).

a(1)=1, a(2)=2, a(3)=3; for n >= 3, a(n) is smallest number such that all a(i) for 1 <= i <= n are distinct, all a(i)+a(j) for 1 <= i < j <= n are distinct and all a(i)+a(j)+a(k) for 1 <= i < j < k <= n are distinct.

Numerator of fraction equal to the continued fraction [0,2,4,...2n].

Denominator of fraction equal to the continued fraction [ 0, 2, 4, ...2n ].

Denominator of continued fraction given by C(n) = [1; 3, 5, 7, ..., (2*n-1)].

Numerator of fraction equal to the continued fraction [ 0, 1, 4, ..., n^2 ].

CONTINUANT transform of squares 1, 4, 9, ...

Numerator of fraction equal to the continued fraction [ 2, 3, 5, ...prime(n) ].

Denominator of fraction equal to the continued fraction [ 2, 3, 5, ..., prime(n) ].

Number of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.)

Number of trees of nonempty sets with n points. (Each node is a set of 1 or more points.)

Number of trees with 2-colored leaves.

Number of trees with 3-colored leaves.

Numerator of fraction equal to the continued fraction [ 3, 1, 4, 1, 5... ] (first n digits of Pi).

Denominator of fraction equal to the continued fraction [ 3, 1, 4, 1, 5... ] (first n digits of Pi).

Number of inequivalent strings of 2n+1 digits, when 2 strings are equivalent if turning 1 upside down gives the other.

a(n) = Sum_{i=0..n} binomial(i,floor(i/2)).

Number of inequivalent strings of 2n digits, when 2 strings are equivalent if turning 1 upside down gives the other.

Number of inequivalent strings of n digits, when 2 strings are equivalent if turning 1 upside down gives the other.

Numbers k such that the multiplicative order of 2 modulo k is odd.

Numbers k > 1 such that k mod ord2(k) is even, where ord2(k) is the order of 2 mod k.