A093623 - OEIS

%I #10 Nov 14 2019 16:37:18

%S 1,1,2,1,1,3,2,6,3,1,8,1,4,3,3,3,5,3,15,13,13,10,8,4,5,12,14,1,2,1,1,

%T 5,13,11,11,1,25,4,2,32,3,4,15,9,10,34,16,3,5,23,13,30,3,13,7,34,3,21,

%U 22,9,10,15,7,26,51,42,18,6,6,31,23,31,51,12,20,8,24,50,40,4,30,49,36,4,23

%N Smallest k>0 such that n!/k!-1 is prime.

%C a(A002982(n)) = 1. The existence of a solution has been checked up to n=500.

%C The results were computed using the PrimeFormGW (PFGW) primality-testing program. - _Hugo Pfoertner_, Nov 14 2019

%e a(10) = 6 because 10!/6! - 1 = 5039 is prime, whereas 10!/k! - 1 is composite for k = 1..5.

%Y Cf. A093622 largest prime of the form n!/k!-1, A002982 n!-1 is prime, A093621 smallest k>0 such that n!/k!+1 is prime.

%K nonn

%O 3,3

%A _Hugo Pfoertner_, Apr 06 2004

%E a(53) corrected by _Gionata Neri_, Jul 18 2017