A057217 a(n) = smallest positive integer k such that 1 + n*k! is a prime.

1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 4, 2, 2, 1, 2, 4, 3, 2, 3, 1, 2, 1, 7, 3, 2, 6, 2, 1, 3, 3, 2, 1, 2, 1, 4, 2, 3, 1, 3, 2, 5, 2, 2, 1, 2, 2, 3, 2, 5, 1, 11, 1, 3, 3, 2, 5, 2, 1, 4, 2, 2, 1, 5, 1, 3, 2, 2, 3, 3, 1, 14, 5, 2, 1, 2, 4, 7, 2, 3, 1, 2, 2, 3, 8, 5, 7, 2, 1, 11, 2, 2, 1, 3, 1, 3

Offset: 1

Author

Labos Elemer, Sep 27 2000

Keywords

• nonn

Examples

			For n = 7, 1 + 7*k! = {8,15,43,169,...}. The smallest k that gives prime is 3 and the obtained prime is 43.
For n = 267, the smallest k! is 31! for which 1 + 267*k! is prime and the obtained prime is 65782709233423382541804503040000001.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Programs

Mathematica

spi[n_]:=Module[{k=1},While[!PrimeQ[1+k!*n],k++];k]; Array[spi,110] (* Harvey P. Dale, May 01 2016 *)

PARI

a(n) = k = 1; while (!isprime(1+n*k!), k++); k; \\ Michel Marcus, Feb 20 2016

Formula

a(n) = Min{k | 1 + nk! is prime}.

Extensions

Offset corrected by Michel Marcus, Feb 20 2016