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 A182662 #27 Apr 04 2014 18:43:18
%S A182662 0,0,1,0,1,0,1,2,1,1,1,0,3,2,1,1,4,3,1,1,3,3,2,3,3,1,2,3,4,2,1,6,4,4,
%T A182662 1,4,2,1,5,4,2,1,2,4,2,2,3,3,3,4,2,3,3,2,3,1,5,2,3,1,5,6,4,5,3,3,1,4,
%U A182662 3,2,3,5,3,3,7,4,3,1,4,5,4,3,2,4,2,5,5,4,2,2,6,8,2,2,4,2,6,1,3,2
%N A182662 Number of ordered ways to write n = p + q with q > 0 such that p, 3*(p + prime(q)) - 1 and 3*(p + prime(q)) + 1 are all prime.
%C A182662 Conjecture: a(n) > 0 if n is not a divisor of 12.
%C A182662 Clearly, this implies the twin prime conjecture.
%H A182662 Zhi-Wei Sun, <a href="/A182662/b182662.txt">Table of n, a(n) for n = 1..10000</a>
%H A182662 Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e A182662 a(11) = 1 since 11 = 7 + 4 with 7, 3*(7 + prime(4)) - 1 = 3*14 - 1 = 41 and 3*(7 + prime(4)) + 1 = 3*14 + 1 = 43 all prime.
%e A182662 a(210) = 1 since 210 = 97 + 113 with 97, 3*(97 + prime(113)) - 1 = 3*(97 + 617) - 1 = 2141 and 3*(97 + prime(113)) + 1 = 3*(97 + 617) + 1 = 2143 all prime.
%t A182662 p[n_,m_]:=PrimeQ[3(m+Prime[n-m])-1]&&PrimeQ[3(m+Prime[n-m])+1]
%t A182662 a[n_]:=Sum[If[p[n,Prime[k]],1,0],{k,1,PrimePi[n-1]}]
%t A182662 Table[a[n],{n,1,100}]
%Y A182662 Cf. A000040, A001359, A006512, A236531, A236831.
%K A182662 nonn
%O A182662 1,8
%A A182662 _Zhi-Wei Sun_, Jan 31 2014