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 A344963 #35 Jun 26 2021 17:28:37
%S A344963 0,2,3,5,11,18,68,77,124,173,205,293,1037,1530,1905,2342,3401,4372,
%T A344963 4679,5385
%N A344963 Numbers k such that (2*k+1)*k!+1 is prime.
%C A344963 a(21) > 10^4.
%p A344963 select(k -> isprime((2*k+1)*k!+1), [$0 .. 300])[];
%t A344963 Do[If[PrimeQ[(2*k + 1)*Factorial[k] + 1], Print[k]], {k, 0, 3000}]
%o A344963 (PARI) for(k=0, 3000, if(isprime((2*k+1)*k!+1), print1(k", ")))
%o A344963 (SageMath)
%o A344963 for k in range(3000):
%o A344963 if is_prime((2*k+1)*factorial(k) + 1):
%o A344963 print(k)
%Y A344963 Cf. A002981, A344991.
%K A344963 nonn,hard,more
%O A344963 1,2
%A A344963 _Reza K Ghazi_, Jun 07 2021