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

0,5

Links

Table of n, a(n) for n=0..64.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A002981

Sequence in context: A267573 A345282 A369749 * A304409 A081732 A079033

Adjacent sequences: A193811 A193812 A193813 * A193815 A193816 A193817

Keyword

nonn

Author

Michel Lagneau, Aug 06 2011

Status

approved