This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A093623 #10 Nov 14 2019 16:37:18 %S A093623 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 A093623 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 A093623 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 A093623 Smallest k>0 such that n!/k!-1 is prime. %C A093623 a(A002982(n)) = 1. The existence of a solution has been checked up to n=500. %C A093623 The results were computed using the PrimeFormGW (PFGW) primality-testing program. - _Hugo Pfoertner_, Nov 14 2019 %e A093623 a(10) = 6 because 10!/6! - 1 = 5039 is prime, whereas 10!/k! - 1 is composite for k = 1..5. %Y A093623 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 A093623 nonn %O A093623 3,3 %A A093623 _Hugo Pfoertner_, Apr 06 2004 %E A093623 a(53) corrected by _Gionata Neri_, Jul 18 2017