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 A086137 #11 Jul 29 2017 17:14:46
%S A086137 2,2,2,1,1,1,1,1,0,2,1,1,1,2,1,1,1,0,0,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,
%T A086137 2,0,0,0,1,1,1,0,0,0,1,1,1,1,1,0,0,1,2,0,0,0,1,1,1,0,0,2,0,0,2,1,0,0,
%U A086137 0,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,2,1,1,0,2,0,1,1,0,0,0,1,0,1
%N A086137 Number of primes between p and p+8 if p is prime, i.e., number of primes between 8+A023202(n) and A023202(n).
%e A086137 a(n)=0,1,2 correspond to {p,p+8} prime-pairs either consecutive or pairs with various d-patterns as follows:
%e A086137 a(n)=0 to 89[8]97; a(n)=1 for 29[2,6]37, 53[6,2];
%e A086137 a(n)=2 for 101[2,4,2]109 and once to 3[2,2,4]11.
%t A086137 cp[x_,y_] := Count[Table[PrimeQ[i],{i,x,y}],True] Do[s=Prime[n]; s1=Prime[n+1]; If[PrimeQ[s+d],k=k+1; Print[cp[s+1,s+d-1]]],{n,1,1000}]; k
%Y A086137 Cf. A023302, A046133, A048136, A052165.
%K A086137 nonn
%O A086137 1,1
%A A086137 _Labos Elemer_, Jul 29 2003