A344991 Numbers k such that (2*k+1)*k!-1 is prime.

1, 3, 5, 15, 20, 44, 45, 73, 80, 93, 295, 5395

Offset: 1

Author

Reza K Ghazi, Jun 07 2021

Keywords

• nonn
• hard
• more

Comments

a(13) > 10^4.

Crossrefs

Cf. A002982, A344963.

Programs

Maple

select(k -> isprime((2*k+1)*k!-1), [$1 .. 300])[];

Mathematica

Do[If[PrimeQ[(2*k + 1)*Factorial[k] - 1], Print[k]], {k, 1, 3000}]

PARI

for(k=1, 3000, if(isprime((2*k+1)*k!-1), print1(k", ")))

SageMath

for k in range(1, 3000):
    if is_prime((2*k+1)*factorial(k) - 1):
        print(k)