%I #26 Mar 08 2014 04:35:36
%S 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,
%T 27,30,29,34,30,32,32,42,36,36,44,39,38,40,42,42,42,46,44,46,47,49,48,
%U 52,51,58,58,54,54,56,57,59,60,60,60,71,62,65,65,66,67,71
%N a(n) is the minimum number such that a(n)!/n! - 1 is prime (or 0 if no such number exists).
%C If a(n) = 0, all numbers m!/n! - 1 for integer m > n are composite.
%C Up to n = 2500, a(n) > 0.
%H Lei Zhou, <a href="/A238505/b238505.txt">Table of n, a(n) for n = 0..2500</a>
%e n = 1: 2!/1! - 1 = 1 is not prime, 3!/1! - 1 = 5 is prime. So a(1) = 3;
%e 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.
%t Table[i = n; a = n; While[! PrimeQ[a - 1], i++; a = a*i]; i, {n, 1, 67}]
%o (PARI) a(n) = {m = n; while(! isprime(m!/n! -1), m++); m;} \\ _Michel Marcus_, Mar 06 2014
%Y Cf. A000142, A231901
%K nonn
%O 0,1
%A _Lei Zhou_, Feb 27 2014