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 A193814 #12 Oct 10 2019 04:02:06
%S A193814 0,0,0,0,4,6,6,10,22,16,10,0,28,66,18,42,22,30,36,88,28,30,30,96,130,
%T A193814 40,58,0,66,222,106,126,78,36,96,60,130,0,42,96,52,0,96,70,46,238,100,
%U A193814 232,52,82,60,270,52,70,222,70,148,106,282,292,270,768,130,270,66
%N A193814 Least k such that n! + k + 1 is a prime.
%F A193814 a(n) = 0 for n in A002981. - _Michel Marcus_, Oct 10 2019
%e A193814 a(5) = 6 because 5! + 6 + 1 = 127 is prime.
%t A193814 a={};Do[k = 0; While[ !PrimeQ[n! + k + 1], k++ ]; AppendTo[a, k], {n, 0, 70} ];a
%t A193814 ld[n_]:=Module[{f=n!},NextPrime[f]-f-1]; Array[ld,70,0] (* _Harvey P. Dale_, Jul 13 2014 *)
%o A193814 (PARI) a(n) = my(k=0); while (!isprime(n!+k+1), k++); k; \\ _Michel Marcus_, Oct 10 2019
%Y A193814 Cf. A002981
%K A193814 nonn
%O A193814 0,5
%A A193814 _Michel Lagneau_, Aug 06 2011