A374901 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

EXAMPLE

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

PROG

(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

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

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

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

STATUS

approved