Sequences

Smallest number with reciprocal of period length n in decimal (base 10).

Number of non-Abelian (finite) groups with n conjugacy classes.

Beginnings of periodic unitary aliquot sequences.

a(n) = 3^(n-1) - 2^n.

a(n) = smallest number with shortest addition chain of length n.

Number of integers with a shortest addition chain of length n.

Problimes (first definition).

Problimes (second definition).

Problimes (third definition).

Number of n-node digraphs with same converse as complement.

a(n) = ceiling(log_2 n!).

Sorting numbers: maximal number of comparisons for sorting n elements by list merging.

Numbers that are the sum of 3 positive cubes.

A nonlinear recurrence.

Number of different numbers <= n that are sums of 3 positive cubes.

Minimal number of comparisons needed for n-element sorting network.

n-th digit after decimal point of square root of n.

Decimal expansion of 22/7 - Pi.

Number of letters in n (in Danish).

One of the basic cycles in the x->3x-1 (x odd) or x/2 (x even) problem.

Number of rooted triangular cacti with 2n+1 nodes (n triangles).

Number of triangular cacti with 2n+1 nodes (n triangles).

Number of multigraphs with 4 nodes and n edges.

Sum a(n) x^n / n = log (1 + Sum g(n) x^n ), where g(n) is # graphs on n nodes (A000088).

Related to number of digraphs.

Number of weakly connected digraphs with n unlabeled nodes.

Number of self-complementary digraphs with n nodes.

Number of acyclic digraphs with n unlabeled nodes.

Number of unilateral digraphs with n unlabeled nodes.

Number of connected line graphs with n nodes.

Number of species (or "main classes" or "paratopy classes") of Latin squares of order n.

a(n) = floor( 2^(n*(n-1)/2) / n! ).

Number of labeled plane 2-trees with n nodes.

Number of planar 2-trees with n nodes.

Number of unlabeled connected planar simple graphs with n nodes.

a(n) = a(n-1)^2 + 1 for n >= 1, with a(0) = 0.

a(n) = a(n-1)^2 - 1, a(0) = 2.

Critical connected topologies with n points.

Palindromic triangular numbers.

a(n) = Sum_{k=0..n} binomial(n,k^2).

Decimal Gray code for n.

a(n) = Sum_{k = 1..n} (n - k + 1)^k.

Largest number divisible by all numbers < its n-th root.

Number of letters in NATO phonetic alphabet: Alpha, Bravo, Charlie, Delta, Echo, Foxtrot, Golf, Hotel, India, Juliet, Kilo, Lima, Mike, November, Oscar, Papa, Quebec, Romeo, Sierra, Tango, Uniform, Victor, Whiskey, Xray, Yankee, Zulu.

Number of hexagonal n-element polyominoes whose graph is a path.

Schur's 1926 partition theorem: number of partitions of n into parts 6n+1 or 6n-1.

Number of partitions of n into parts 5k+2 or 5k+3.

Number of partitions of n into Fibonacci parts (with a single type of 1).

Number of partitions of n into cubes.

a(n) = number of special even permutations of 2*n+1.