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

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