cp's OEIS Frontend

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

%I A374901 #33 Oct 03 2024 03:54:36
%S A374901 1,3,4,6,10,11,118,271,288,441,457,2931,5527,6984,9998,10395,13703
%N A374901 Numbers k such that k!^2 + ((k - 1)!^2) + 1 is prime.
%C A374901 a(18) > 15000 - _Karl-Heinz Hofmann_, Aug 23 2024
%e A374901 4 is a term, because 4!^2 + 3!^2 + 1 = 576 + 36 + 1 = 613 is a prime number.
%o A374901 (PARI) is(k) = isprime((k!^2)+((k-1)!)^2+1);
%o A374901 (Python)
%o A374901 from itertools import count, islice
%o A374901 from sympy import isprime
%o A374901 def A374901_gen(): # generator of terms
%o A374901     f = 1
%o A374901     for k in count(1):
%o A374901         if isprime((k**2+1)*f+1):
%o A374901             yield k
%o A374901         f *= k**2
%o A374901 A374901_list = list(islice(A374901_gen(),10)) # _Chai Wah Wu_, Oct 02 2024
%Y A374901 Cf. A000142, A055490, A358805, A358878, A359180, A080778, A243078, A242994
%K A374901 nonn,more
%O A374901 1,2
%A A374901 _Arsen Vardanyan_, Jul 31 2024
%E A374901 a(12)-a(14) from _Michael S. Branicky_, Aug 01 2024
%E A374901 a(15)-a(17) from _Karl-Heinz Hofmann_, Aug 23 2024