Sequences

Number of 1 digits in base 3 representation of 2^n.

Conjecturally, a power of 2 written in base 3 cannot have this many 0's.

Conjecturally, a power of 2 written in base 3 cannot have this many 2's.

Number of ways to place two nonattacking queens on an n X n board.

If n^2 = Sum_{i} b(i)^2 for positive integers b(i) < n, then a(n) is the maximum value of min(b(i)).

If n = Sum_{i} b(i)^2 (i.e., a partition of n into squares), then a(n) is the smallest possible value of the largest multiplicity of the b(i).

a(n) + a(n-1) = n-th prime.

Number of ways to represent 2n+1 as a+b with 0 < a < b and a^2 + b^2 prime.

Partial sums of A000009 (partitions into distinct parts).

a(n) is the number of distinct possible values of d(k), the number of divisors of k, among numbers k whose binary order (A029837) does not exceed n.

Four numbers (a,b,c,d) with a<b<c<d that satisfy sigma(a) = sigma(b) = sigma(c) = sigma(d) = a+b+c+d are called an amicable quadruple. We order these quadruples according to the common value of sigma. The values of (a, b, c, d, sigma) are in (this sequence, A036472, A036473, A036474, A116148) respectively.

Amicable quadruples: the numbers b referred to in A036471.

Amicable quadruples: the numbers c referred to in A036471.

Amicable quadruples: the numbers d referred to in A036471.

a(n) = partition(11n+1) mod 11.

a(n) = partition(11n+2) mod 11.

a(n) = partition(11n+3) mod 11.

a(n) = partition(11n+4) mod 11.

a(n) = partition(11n+5) mod 11.

a(n) = partition(11n+7) mod 11.

a(n) = partition(11n+8) mod 11.

a(n) = partition(11n+9) mod 11.

a(n) = partition(11n+10) mod 11.

a(n) is the minimal number of binary order n which has maximal number of divisors in this interval.

a(n) = partition(11n) mod 11.

a(n) = ceiling((n^3)/2).

a(n) = floor((n^3)/2).

Nearest integer to n^(5/2).

Nearest integer to n^(7/2).

Numbers whose prime factors are in {5, 7, 11}.

Transformation of A036490: 5^a*7^b*11^c -> 5^a*7^floor((b+2)/2)*11^c.

Offsets for the Atkin Partition Congruence theorem.

Largest number having binary order n (A029837) and of which the number of divisors is maximal in that range of g(k) = n.

Nearest integer to n^(9/2).

Nearest integer to n^(11/2).

Number of lines that intersect the first n points on a spiral on a triangular lattice. The spiral starts at (0,0), goes to (1,0) and (1/2, sqrt(3)/2) and continues counterclockwise.

Number of partitions of n into distinct primes (counting 1 as a prime).

Numbers of the form m*(6*m-1) and m*(6*m+1), where m is an integer.

Numbers of the form k*(k+1)/6 for k = 2 or 3 modulo 6.

Number of inequivalent cyclic Hadamard difference sets with parameters (2^n-1, 2^(n-1)-1, 2^(n-2)-1).

Number of inequivalent Golomb rulers with n marks and shortest length.

Numerator of n^(n-2)/n!.

Denominator of n^(n-2)/n!.

Numerator of n^(n-1)/n!.

Numerator of (n+1)^n/n!.

Number of labeled 4-trees with n nodes.

Smallest square containing exactly n decimal digits '0'.

Smallest square containing exactly n 1's.

Smallest square containing exactly n 2's.

Smallest square containing exactly n 3's.