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Numbers n such that Sum_{k=1..n} k! - 2 is prime.
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%I #8 Nov 15 2014 09:24:18

%S 3,4,5,12,13,19,65,90,123,211,281,459

%N Numbers n such that Sum_{k=1..n} k! - 2 is prime.

%C There are no further terms in this sequence because for all n >= 466 (Sum_{k=1..n} k!) - 2 is divisible by 467. [From _Dmitry Kamenetsky_, Feb 10 2009]

%e 1! + 2! + 3! + 4! + 5! -2 = 1 + 2 + 6 + 24 + 120 - 2 = 151 which is a prime.

%t Do[If[PrimeQ[Sum[m!, {m, 1, n}]-2], Print[n]], {n, 1, 2500}]

%t Flatten[Position[Accumulate[Range[500]!]-2,_?PrimeQ]] (* _Harvey P. Dale_, Nov 15 2014 *)

%K nonn,fini,full

%O 1,1

%A _Robert G. Wilson v_, Jul 05 2000