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 A231516 #25 Nov 12 2013 02:33:16
%S A231516 0,1,1,1,2,1,2,3,1,3,2,1,3,3,3,4,3,3,2,5,4,2,6,4,3,4,2,4,8,4,5,4,7,5,
%T A231516 6,5,5,7,4,7,7,4,10,5,3,6,8,7,7,7,7,5,8,5,5,8,4,6,8,4,7,3,7,5,6,6,5,3,
%U A231516 9,5,12,2,10,4,4,7,7,8,7,8,7,10,8,5,4,7,12,9,6,6,6,7,3,12,5,7,8,10,8,6
%N A231516 Number of ways to write n = x + y with 0 < x <= y such that x!*y + 1 is prime.
%C A231516 Conjecture: a(n) > 0 for all n > 1. Also, any integer n > 3 can be written as x + y with 0 < x <= y such that x!*y -1 is prime.
%C A231516 We have verified the conjecture for n up to 10^6.
%H A231516 Zhi-Wei Sun, <a href="/A231516/b231516.txt">Table of n, a(n) for n = 1..2000</a>
%e A231516 a(9) = 1 since 9 = 3 + 6 with 3!*6 + 1 = 37 prime.
%e A231516 a(12) = 1 since 12 = 4 + 8 with 4!*8 + 1 = 193 prime.
%t A231516 a[n_]:=Sum[If[PrimeQ[x!*(n-x)+1],1,0],{x,1,n/2}]
%t A231516 Table[a[n],{n,1,100}]
%Y A231516 Cf. A000040, A000142, A231201, A231555, A231561, A231557, A231631.
%K A231516 nonn
%O A231516 1,5
%A A231516 _Zhi-Wei Sun_, Nov 11 2013