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