A064983 a(n) is the smallest prime p such that p*n! - 1 is prime.

3, 3, 2, 2, 2, 2, 2, 2, 5, 3, 29, 11, 3, 5, 2, 2, 53, 2, 67, 79, 5, 61, 2, 7, 13, 5, 3, 11, 2, 107, 43, 7, 31, 199, 293, 17, 43, 197, 109, 41, 13, 277, 11, 167, 17, 83, 157, 31, 199, 131, 13, 5, 89, 47, 223, 83, 43, 7, 139, 151, 211, 19, 19, 23, 43, 311, 61, 53, 191, 163, 11

Offset: 0

Author

Robert G. Wilson v, Oct 30 2001

Keywords

• nonn

Comments

The PFGW program has been used to certify all the primes corresponding to the terms up to a(1000), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, May 30 2018

Links

• Giovanni Resta, Table of n, a(n) for n = 0..1000 (terms 0..200 from Harry J. Smith)

Crossrefs

Cf. A051888.

Programs

Mathematica

Do[k = 1; While[ !PrimeQ[ Prime[k]*n! - 1], k++ ]; Print[ Prime[k]], {n, 1, 75} ]

PARI

{ allocatemem(932245000); for (n=0, 200, f=n!; k=1; while(!isprime(prime(k)*f - 1), k++); write("b064983.txt", n, " ", prime(k)) ) } \\ Harry J. Smith, Oct 02 2009