OFFSET
1,1
COMMENTS
Contains no primes. - Robert Israel, Aug 12 2024
Moreover: If k is any prime, then k must divide the given formula and if k is not a prime the least factor that divides the formula is bigger than k and smaller than the square root of the result of the formula (if it exist, if not: k is a term). - Karl-Heinz Hofmann, Aug 20 2024
a(11) > 15000. - Karl-Heinz Hofmann, Sep 08 2024
EXAMPLE
14 is a term, because 14!^2 + 13!^2 - 1 = 7600054456551997440000 + 38775788043632640000 - 1 = 7638830244595630079999 is a prime number.
MAPLE
select(k -> isprime((k^2+1)*((k-1)!)^2-1), [$1..1000]); # Robert Israel, Aug 12 2024
PROG
(PARI) is(k) = isprime(k!^2 + (k-1)!^2 - 1);
(Python)
from itertools import count, islice
from sympy import isprime
def A375310_gen(): # generator of terms
f = 1
for k in count(1):
if isprime((k**2+1)*f-1):
yield k
f *= k**2
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Arsen Vardanyan, Aug 11 2024
EXTENSIONS
a(8) from Hugo Pfoertner, Aug 13 2024
a(9) from Michael S. Branicky, Aug 14 2024
a(10) from Karl-Heinz Hofmann, Sep 08 2024
STATUS
approved