A075757 Smallest positive integer k such that n!+k!+1 is prime, or 0 if no such k exists.
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, 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, 107, 57, 27, 55, 0, 55, 0, 27, 29, 0, 79, 0, 45, 61, 48, 55, 39, 80, 56, 153, 76, 0, 35, 11
Offset: 1
Keywords
Examples
3!=6, 6+1!+1=8, 6+2!+1=9, 6+3!+1=13, which is prime, so a(3)=3.
Programs
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Mathematica
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 <
Extensions
Edited by Dean Hickerson, Oct 10 2002
The fact that 73!+153!+1 is prime, so a(73)=153, was proved, using Primo, by Robert G. Wilson v, Oct 16 2002