A193814 Least k such that n! + k + 1 is a prime.

0, 0, 0, 0, 4, 6, 6, 10, 22, 16, 10, 0, 28, 66, 18, 42, 22, 30, 36, 88, 28, 30, 30, 96, 130, 40, 58, 0, 66, 222, 106, 126, 78, 36, 96, 60, 130, 0, 42, 96, 52, 0, 96, 70, 46, 238, 100, 232, 52, 82, 60, 270, 52, 70, 222, 70, 148, 106, 282, 292, 270, 768, 130, 270, 66

Offset: 0

Author

Michel Lagneau, Aug 06 2011

Keywords

• nonn

Examples

			a(5) = 6 because 5! + 6 + 1 = 127 is prime.
		

Crossrefs

Cf. A002981

Programs

Mathematica

a={};Do[k = 0; While[ !PrimeQ[n! + k + 1], k++ ]; AppendTo[a, k], {n, 0, 70} ];a
ld[n_]:=Module[{f=n!},NextPrime[f]-f-1]; Array[ld,70,0] (* Harvey P. Dale, Jul 13 2014 *)

PARI

a(n) = my(k=0); while (!isprime(n!+k+1), k++); k; \\ Michel Marcus, Oct 10 2019

Formula

a(n) = 0 for n in A002981. - Michel Marcus, Oct 10 2019