cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A101747 Numbers n such that ((0!)^2+(1!)^2+(2!)^2+...+(n!)^2)/6 is prime.

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%I A101747 #9 Sep 04 2022 11:26:51
%S A101747 3,4,5,6,7,19,40,56,93
%N A101747 Numbers n such that ((0!)^2+(1!)^2+(2!)^2+...+(n!)^2)/6 is prime.
%C A101747 Let S(n) = Sum_{i=0,..n-1} (i!)^2. Note that 6 divides S(n) for n>1. For prime p=20879, p divides S(p-1). Hence p divides S(n) for all n >= p-1 and all prime values of S(n)/6 are for n < p-1. These n yield provable primes for n <= 93. No other n < 4000.
%C A101747 No other n < 8000. [_T. D. Noe_, Jul 31 2008]
%t A101747 f2=1; s=2; Do[f2=f2*n*n; s=s+f2; If[PrimeQ[s/6], Print[{n, s/6}]], {n, 2, 100}]
%Y A101747 Cf. A061062 (S(n)), A100288 (primes of the form S(n)-1), A100289 (n such that S(n)-1 is prime), A101746 (primes of the form S(n)/6).
%K A101747 fini,nonn
%O A101747 1,1
%A A101747 _T. D. Noe_, Dec 18 2004