A238505 a(n) is the minimum number such that a(n)!/n! - 1 is prime (or 0 if no such number exists).

3, 3, 3, 4, 6, 6, 9, 8, 10, 11, 12, 12, 14, 14, 16, 17, 19, 18, 20, 20, 22, 24, 25, 24, 41, 27, 30, 29, 34, 30, 32, 32, 42, 36, 36, 44, 39, 38, 40, 42, 42, 42, 46, 44, 46, 47, 49, 48, 52, 51, 58, 58, 54, 54, 56, 57, 59, 60, 60, 60, 71, 62, 65, 65, 66, 67, 71

Offset: 0

Author

Lei Zhou, Feb 27 2014

Keywords

• nonn

Comments

If a(n) = 0, all numbers m!/n! - 1 for integer m > n are composite.

Up to n = 2500, a(n) > 0.

Examples

			n = 1: 2!/1! - 1 = 1 is not prime, 3!/1! - 1 = 5 is prime.  So a(1) = 3;
n = 6: 7!/6! - 1 = 6, 8!/6! - 1 = 55, 9!/6! - 1 = 503.  6 and 55 are not prime.  503 is prime.  So a(6) = 9.
		

Links

• Lei Zhou, Table of n, a(n) for n = 0..2500

Crossrefs

Cf. A000142, A231901

Programs

Mathematica

Table[i = n; a = n;  While[! PrimeQ[a - 1], i++; a = a*i]; i, {n, 1, 67}]

PARI

a(n) = {m = n; while(! isprime(m!/n! -1), m++); m;} \\ Michel Marcus, Mar 06 2014