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.
%I A376644 #13 Oct 03 2024 23:34:56
%S A376644 1,2,4,6,13,14,21,41,64,110,268,1196,3083,5201,7496,9698
%N A376644 Numbers k such that !k * k! + 1 = A003422(k) * A000142(k) + 1 = A061640(k) + 1 is prime.
%C A376644 a(1)-a(11) were found by Earls (2003-2004).
%C A376644 The corresponding primes are 2, 5, 241, 110881, 3256459844769331201, ... .
%H A376644 Jason Earls, <a href="https://www.proquest.com/openview/4375c07dc57d66a121a0bd7bcf5f86d5/1?pq-origsite=gscholar&cbl=31970">Marching Primes: !N x N! + 1</a>, Journal of Recreational Mathematics, Vol. 32, No. 2 (2003-2004), pp. 123-124.
%t A376644 Select[Range[300], PrimeQ[#! * Sum[k!, {k, 0, #-1}] + 1] &]
%o A376644 (PARI) is(k) = isprime(k! * sum(i = 0, k-1, i!) + 1);
%Y A376644 Cf. A000142, A003422, A061640.
%K A376644 nonn,more
%O A376644 1,2
%A A376644 _Amiram Eldar_, Oct 01 2024
%E A376644 a(14)-a(16) from _Michael S. Branicky_, Oct 03 2024