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 A071414 #4 Mar 30 2012 17:22:25
%S A071414 1,1,2,1,2,2,2,1,3,1,2,4,2,2,6,2,2,7,3,4,5,3,2,6,3,3,5,4,3,8,2,5,9,5,
%T A071414 5,6,4,3,7,5,4,10,3,5,11,6,5,9,5,7,10,5,5,5,5,6,11,3,6,15,3,6,12,4,6,
%U A071414 11,8,4,11,9,4,10,6,6,16,6,7,16,7,8,11,6,6,15,9,8,12,8,8,13,9,5,14,7,12
%N A071414 Number of times 4n+r and 2n+r are both prime, with 0 < r < 2n.
%C A071414 Related to the even terms of A070897. If a(n)>0 then there is a simple pairing whose sums involve just 1 (if r=1) or 2 primes. For the case n=2, which corresponds to A070897(4), the numbers 1,2,3,4 can be paired with 5,6,7,8 so that the sums are 11 and 7 (the primes obtained when r=3).
%e A071414 a(3)=2 because 12+r and 6+r are both prime for only 2 values of r: 1 and 5.
%t A071414 For[lst={}; n=1, n<=100, n++, cnt=0; For[k=1, k<2n, k=k+2, If[PrimeQ[4n+k]&&PrimeQ[2n+k], cnt++ ]]; AppendTo[lst, cnt]]; lst
%K A071414 easy,nonn
%O A071414 1,3
%A A071414 _T. D. Noe_, May 29 2002