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%I #8 Jun 24 2014 01:08:26
%S 1,2,3,3,3,3,8,7,10,9,17,7,9,8,19,7,11,11,15,15,11,14,7,20,31,13,7,0,
%T 13,0,25,20,7,23,23,21,7,19,21,0,52,7,23,13,13,17,50,8,76,19,51,41,7,
%U 107,57,27,55,0,55,0,27,29,0,79,0,45,61,48,55,39,80,56,153,76,0,35,11
%N Smallest positive integer k such that n!+k!+1 is prime, or 0 if no such k exists.
%e 3!=6, 6+1!+1=8, 6+2!+1=9, 6+3!+1=13, which is prime, so a(3)=3.
%t a[1]=1; a[n_] := For[k=2, True, k++, If[Mod[n!+1, k]==0, Return[0]]; If[ProvablePrimeQ[n!+k!+1], Return[k]]] (* First do <<NumberTheory`PrimeQ` *)
%K nonn
%O 1,2
%A _Jon Perry_, Oct 08 2002
%E Edited by _Dean Hickerson_, Oct 10 2002
%E The fact that 73!+153!+1 is prime, so a(73)=153, was proved, using Primo, by _Robert G. Wilson v_, Oct 16 2002