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 A075757 Smallest positive integer k such that n!+k!+1 is prime, or 0 if no such k exists. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE 3!=6, 6+1!+1=8, 6+2!+1=9, 6+3!+1=13, which is prime, so a(3)=3. 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 <

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Last modified June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)