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

1,3

Links

Table of n, a(n) for n=1..103.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A326975 A204893 A251717 * A193330 A147810 A305302

Adjacent sequences: A057214 A057215 A057216 * A057218 A057219 A057220

Keyword

nonn

Author

Labos Elemer, Sep 27 2000

Extensions

Offset corrected by Michel Marcus, Feb 20 2016

Status

approved