A057217 - OEIS

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

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OFFSET

1,3

LINKS

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

FORMULA

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

EXAMPLE

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.

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,changed

AUTHOR

Labos Elemer, Sep 27 2000

EXTENSIONS

Offset corrected by Michel Marcus, Feb 20 2016

STATUS

approved