A374901 Numbers k such that k!^2 + ((k - 1)!^2) + 1 is prime.

1, 3, 4, 6, 10, 11, 118, 271, 288, 441, 457, 2931, 5527, 6984, 9998, 10395, 13703

Offset: 1

Author

Arsen Vardanyan, Jul 31 2024

Keywords

• nonn
• more

Comments

a(18) > 15000 - Karl-Heinz Hofmann, Aug 23 2024

Examples

			4 is a term, because 4!^2 + 3!^2 + 1 = 576 + 36 + 1 = 613 is a prime number.
		

Crossrefs

Cf. A000142, A055490, A358805, A358878, A359180, A080778, A243078, A242994

Programs

PARI

is(k) = isprime((k!^2)+((k-1)!)^2+1);

Python

from itertools import count, islice
from sympy import isprime
def A374901_gen(): # generator of terms
    f = 1
    for k in count(1):
        if isprime((k**2+1)*f+1):
            yield k
        f *= k**2
A374901_list = list(islice(A374901_gen(),10)) # Chai Wah Wu, Oct 02 2024

Extensions

a(12)-a(14) from Michael S. Branicky, Aug 01 2024

a(15)-a(17) from Karl-Heinz Hofmann, Aug 23 2024