Sequences

An equivalence relation on permutations.

A Beatty sequence: floor( n * (1 + sqrt(3))/2 ).

A Beatty sequence: floor(n*(sqrt(3) + 2)).

Number of regular sequences of length n.

Number of series-reduced labeled graphs with n nodes.

Number of series-reduced connected labeled graphs with n nodes.

Binomial coefficients C(2n+1, n-2).

Number of permutations of [n+1] with exactly 1 increasing subsequence of length 3.

a(n) = 8*binomial(2*n+1,n-3)/(n+5).

a(n) = 10*binomial(2*n + 1, n - 4)/(n + 6).

a(n) = a(n-1) + a(n-5); a(0) = ... = a(4) = 1.

Values of m in the discriminant D = -4*m leading to a new minimum of the L-function of the Dirichlet series L(1) = Sum_{k>=1} Kronecker(D,k)/k.

a(n) = Sum_{k=0..n} C(n-k,3k).

Divisors of 2^10 - 1.

Divisors of 2^12 - 1.

Divisors of 2^14 - 1.

Divisors of 2^15 - 1.

Divisors of 2^16 - 1.

Divisors of 2^18 - 1.

Divisors of 2^20 - 1.

Divisors of 2^21 - 1.

Divisors of 2^22 - 1.

Divisors of 2^24 - 1.

Divisors of 2^25 - 1.

Divisors of 2^26 - 1.

Divisors of 2^27 - 1.

Divisors of 2^28 - 1.

Divisors of 2^29 - 1.

Divisors of 2^30 - 1.

a(0) = 587, a(n) = 3*a(n-1) + 16 for n > 0 (the first 11 terms are primes).

Divisors of 2^33 - 1.

Divisors of 2^34 - 1.

Divisors of 2^35 - 1.

Divisors of 2^36 - 1.

Divisors of 2^38 - 1.

Divisors of 2^39 - 1.

Divisors of 2^40 - 1.

Divisors of 2^42 - 1.

Divisors of 2^43 - 1.

Divisors of 2^44 - 1.

Divisors of 2^45 - 1.

Divisors of 2^46 - 1.

Divisors of 2^47 - 1.

Divisors of 2^48 - 1.

Divisors of 2^50 - 1.

Sum_{i=1..(10^n - 1)/9} i, or ((10^n -1)/9)*((10^n -1)/9 +1)/2 (n-th term is the middle 2(n-1) digits of the (n+9)-th term for n > 1).

Numbers that are both square and tetrahedral.

n divided by largest squarefree divisor of n; if n = Product p(k)^e(k) then a(n) = Product p(k)^(e(k)-1), with a(1) = 1.

Least number m > 0 such that 2^m == +-1 (mod 2n + 1).

Least number m such that 3^m == +- 1 (mod 3n + 1).