Sequences

Numbers with an even number of partitions.

a(n) = (7*n+3)*(7*n+5)*(7*n+6).

Numbers n such that (10^n + 1)/11 is a prime.

a(n) = n*n! = (n+1)! - n!.

2nd differences of factorial numbers.

3rd differences of factorial numbers.

a(0) = 3; thereafter, a(n) = a(n-1)^2 - 2.

Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers.

Related to 3-line Latin rectangles.

Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*(1-exp(x))^(1/2)).

Numbers k such that k^2 is centered hexagonal.

a(n) = 4*a(n-1) - a(n-2) + 1, with a(0) = 0, a(1) = 2.

Related to series-parallel networks.

Another approximation to A000084(n).

Colored series-parallel networks.

Colored series-parallel networks.

a(n) = 1^n + 2^n + 4^n.

An operational recurrence.

Smallest primitive prime factor of Fibonacci number F(n), or 1 if F(n) has no primitive prime factor.

a(n) = 3^n + 5^n + 6^n.

a(n) = 2^n + n^2.

Winning moves in Fibonacci nim.

Product of Fibonacci and Pell numbers.

Artiads: the primes p == 1 (mod 5) for which Fibonacci((p-1)/5) is divisible by p.

A generalized Fibonacci sequence.

a(n) = 3^n + n^3.

Generalized Euler numbers, or Springer numbers.

Generalized Euler numbers.

a(n) = a(n-1) + a(n-2) - 1.

a(n) = 4^n + n^4.

Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=0, a(1)=1, a(2)=0.

Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5), a(0)=a(1)=a(2)=a(3)=0, a(4)=1.

Hexanacci numbers: a(n+1) = a(n)+...+a(n-5) with a(0)=...=a(4)=0, a(5)=1.

a(n) = 5^n + n^5.

a(n) = 6^n + n^6.

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

a(n) = 7^n + n^7.

Perfect powers: m^k where m > 0 and k >= 2.

Number of terms in {b(1)..b(n)} relatively prime to b(n), where b(n) = A001597(n).

Harmonic or Ore numbers: numbers k such that the harmonic mean of the divisors of k is an integer.

Harmonic means of divisors of harmonic numbers.

a(n) = 2*a(n-1)^2 - 1, if n>1. a(0)=1, a(1)=3.

Fibonacci entry points: a(n) = smallest m > 0 such that the n-th prime divides Fibonacci(m).

Odd-indexed terms of A124296.

Odd-indexed terms of A124297.

Indices of prime Fibonacci numbers.

Indices of prime Lucas numbers.

a(n) = -a(n-1) - 2*a(n-2).

Perrin sequence (or Perrin numbers, or Ondrej Such sequence): a(n) = a(n-2) + a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2.

a(1) = a(2) = 1, a(3) = 4; thereafter a(n) = a(n-1) + a(n-3).