A344963 Numbers k such that (2*k+1)*k!+1 is prime.

0, 2, 3, 5, 11, 18, 68, 77, 124, 173, 205, 293, 1037, 1530, 1905, 2342, 3401, 4372, 4679, 5385

Offset: 1

Author

Reza K Ghazi, Jun 07 2021

Keywords

• nonn
• hard
• more

Comments

a(21) > 10^4.

Crossrefs

Cf. A002981, A344991.

Programs

Maple

select(k -> isprime((2*k+1)*k!+1), [$0 .. 300])[];

Mathematica

Do[If[PrimeQ[(2*k + 1)*Factorial[k] + 1], Print[k]], {k, 0, 3000}]

PARI

for(k=0, 3000, if(isprime((2*k+1)*k!+1), print1(k", ")))

SageMath

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