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 A206589 #5 Mar 30 2012 18:58:12
%S A206589 1,0,2,1,2,1,1,1,1,0,3,1,2,1,2,0,2,0,2,1,2,1,1,0,0,1,1,0,4,1,2,2,2,1,
%T A206589 1,1,1,1,3,1,3,1,1,2,1,0,3,1,1,1,1,0,2,1,2,2,1,1,4,0,1,1,0,0,2,0,2,2,
%U A206589 3,0,4,1,2,2,1,1,3,1,2,1,2,1,3,1,3,2,3,1,3,0,1,0,2,1,2,0,2,0,2
%N A206589 Number of solutions (n,k) of p(k+1)=p(n+1) (mod n), where 1<=k<n.
%C A206589 Related to A206588, which includes differences p-2.
%e A206589 For k=1 to 5, the numbers p(7)-p(k+1) are 14,12,10,6,4, so that a(6)=2.
%t A206589 f[n_,k_]:=If[Mod[Prime[n+1]-Prime[k+1],n]==0,1,0];
%t A206589 t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]
%t A206589 a[n_] := Count[Flatten[t[n]], 1]
%t A206589 Table[a[n], {n, 2, 120}] (* A206589 *)
%Y A206589 Cf. A206588.
%K A206589 nonn
%O A206589 2,3
%A A206589 _Clark Kimberling_, Feb 09 2012