A093623 - OEIS

A093623

Smallest k>0 such that n!/k!-1 is prime.

1, 1, 2, 1, 1, 3, 2, 6, 3, 1, 8, 1, 4, 3, 3, 3, 5, 3, 15, 13, 13, 10, 8, 4, 5, 12, 14, 1, 2, 1, 1, 5, 13, 11, 11, 1, 25, 4, 2, 32, 3, 4, 15, 9, 10, 34, 16, 3, 5, 23, 13, 30, 3, 13, 7, 34, 3, 21, 22, 9, 10, 15, 7, 26, 51, 42, 18, 6, 6, 31, 23, 31, 51, 12, 20, 8, 24, 50, 40, 4, 30, 49, 36, 4, 23

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OFFSET

3,3

COMMENTS

a(A002982(n)) = 1. The existence of a solution has been checked up to n=500.

The results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

LINKS

Table of n, a(n) for n=3..87.

EXAMPLE

a(10) = 6 because 10!/6! - 1 = 5039 is prime, whereas 10!/k! - 1 is composite for k = 1..5.

CROSSREFS

Cf. A093622 largest prime of the form n!/k!-1, A002982 n!-1 is prime, A093621 smallest k>0 such that n!/k!+1 is prime.