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%I #48 Jun 26 2021 16:58:39
%S 1,3,5,15,20,44,45,73,80,93,295,5395
%N Numbers k such that (2*k+1)*k!-1 is prime.
%C a(13) > 10^4.
%p select(k -> isprime((2*k+1)*k!-1), [$1 .. 300])[];
%t Do[If[PrimeQ[(2*k + 1)*Factorial[k] - 1], Print[k]], {k, 1, 3000}]
%o (PARI) for(k=1, 3000, if(isprime((2*k+1)*k!-1), print1(k", ")))
%o (SageMath)
%o for k in range(1, 3000):
%o if is_prime((2*k+1)*factorial(k) - 1):
%o print(k)
%Y Cf. A002982, A344963.
%K nonn,hard,more
%O 1,2
%A _Reza K Ghazi_, Jun 07 2021
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