A283563 Numbers n such that A112368(n) = Sum_{i=0..n} 2^i*i! is prime.

1, 2, 3, 4, 5, 6, 11, 18, 22, 71

Offset: 1

Author

Amiram Eldar, Mar 11 2017

Keywords

• nonn
• fini
• full

Comments

All the terms of A112368 starting from a(72) are divisible by 73.

The first 9 associated primes are 3, 11, 59, 443, 4283, 50363, 85662309563, 1726380042510080613563, 4824162806180387282426469563. The 10th and last term is about 2.022... * 10^123.

Examples

			1 is in this sequence because 2^0*0! + 2^1*1! = 3 is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10

Crossrefs

Cf. A112368.

Programs

Mathematica

A112368[n_] := Sum[2^i*i!, {i, 0, n}]; Select[Range[0, 1000], PrimeQ[A112368[#]] &]

PARI

isok(n) = isprime(sum(i=0, n, 2^i*i!)); \\ Michel Marcus, Mar 11 2017