cp's OEIS Frontend

A375310 Numbers k such that k!^2 + (k-1)!^2 - 1 is prime.

%I A375310 #35 Oct 03 2024 06:07:18
%S A375310 14,32,58,182,240,474,824,3018,5977,9088
%N A375310 Numbers k such that k!^2 + (k-1)!^2 - 1 is prime.
%C A375310 Contains no primes. - _Robert Israel_, Aug 12 2024
%C A375310 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
%C A375310 a(11) > 15000. -  _Karl-Heinz Hofmann_, Sep 08 2024
%e A375310 14 is a term, because 14!^2 + 13!^2 - 1 = 7600054456551997440000 + 38775788043632640000 - 1 = 7638830244595630079999 is a prime number.
%p A375310 select(k -> isprime((k^2+1)*((k-1)!)^2-1), [$1..1000]); # _Robert Israel_, Aug 12 2024
%o A375310 (PARI) is(k) = isprime(k!^2 + (k-1)!^2 - 1);
%o A375310 (Python)
%o A375310 from itertools import count, islice
%o A375310 from sympy import isprime
%o A375310 def A375310_gen(): # generator of terms
%o A375310     f = 1
%o A375310     for k in count(1):
%o A375310         if isprime((k**2+1)*f-1):
%o A375310             yield k
%o A375310         f *= k**2
%o A375310 A375310_list = list(islice(A375310_gen(),6)) # _Chai Wah Wu_, Oct 02 2024
%Y A375310 Cf. A374901.
%Y A375310 Cf. A000142, A055490, A358805, A358878, A359180.
%K A375310 nonn,more
%O A375310 1,1
%A A375310 _Arsen Vardanyan_, Aug 11 2024
%E A375310 a(8) from _Hugo Pfoertner_, Aug 13 2024
%E A375310 a(9) from _Michael S. Branicky_, Aug 14 2024
%E A375310 a(10) from _Karl-Heinz Hofmann_, Sep 08 2024