A361437 - OEIS

%I #36 Oct 02 2024 14:21:32

%S 2,3,4,5,6,7,8,12,15,58,59,102,111,118,164,291,589,685,1671,1900,1945,

%T 4905,9564

%N Numbers k such that k! - Sum_{i=1..k-1} (-1)^(k-i)*i! is prime.

%C Numbers k such that k! + A005165(k - 1) is prime.

%C a(23) > 7000. - _Hugo Pfoertner_, Mar 15 2023

%e 2 is in the sequence because 2! + 1! = 3.

%e 3 is in the sequence because 3! + (2! - 1!) = 7.

%e 4 is in the sequence because 4! + (3! - 2! + 1!) = 29.

%e 5 is in the sequence because 5! + (4! - 3! + 2! - 1!) = 139.

%o (PARI) isok(k) = isprime(k! + sum(i=1, k-1, (-1)^(i+1)*(k-i)!)); \\ _Michel Marcus_, Mar 12 2023

%Y Cf. A361436 (the corresponding primes).

%Y Cf. A001272, A005165 (alternating factorials), A071828.

%K nonn,hard,more

%O 1,1

%A _Jack Braxton_, Mar 11 2023

%E Missing a(10) inserted and a(12)-a(18) from _Andrew Howroyd_, Mar 12 2023

%E a(19)-a(22) from _Hugo Pfoertner_, Mar 13 2023

%E a(23) from _Michael S. Branicky_, Oct 02 2024