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 A235187 #6 Jan 04 2014 12:56:39
%S A235187 0,0,1,1,2,1,1,2,2,3,2,3,2,1,2,2,2,3,1,2,5,5,2,5,3,2,5,2,1,6,2,4,4,1,
%T A235187 5,3,4,3,6,6,3,5,5,2,9,3,3,7,2,4,7,6,3,6,7,5,4,4,4,12,3,2,5,3,3,9,3,1,
%U A235187 7,4,2,8,6,3,8,3,4,7,6,3,10,3,3,10,8,3,11,5,3,10,6,1,9,8,2,7,4,3,9,4
%N A235187 Number of ordered ways to write 2*n = p + q with p, q and prime(p) + q - 1 all prime.
%C A235187 Conjecture: (i) a(n) > 0 for all n > 2.
%C A235187 (ii) Any integer n > 4 can be written as p + q with q > 0 such that p and p - 1 + prime(q) are both prime.
%C A235187 (iii) Each integer n > 7 can be written as p + q with q > 0 such that prime(p) + sigma(q) is prime, where sigma(q) denotes the sum of all positive divisors of q.
%C A235187 Clearly, part (i) is stronger than Goldbach's conjecture.
%H A235187 Zhi-Wei Sun, <a href="/A235187/b235187.txt">Table of n, a(n) for n = 1..10000</a>
%e A235187 a(7) = 1 since 2*7 = 7 + 7 with 7 and prime(7) + 7 - 1 = 17 + 6 = 23 both prime.
%e A235187 a(14) = 1 since 2*14 = 11 + 17 with 11, 17 and prime(11) + 16 = 47 all prime.
%e A235187 a(92) = 1 since 2*92 = 47 + 137 with 47, 137 and prime(47) + 136 = 347 all prime.
%t A235187 a[n_]:=Sum[If[PrimeQ[2n-Prime[k]]&&PrimeQ[Prime[Prime[k]]+2n-Prime[k]-1],1,0],{k,1,PrimePi[2n-1]}]
%t A235187 Table[a[n],{n,1,100}]
%Y A235187 Cf. A000040, A000203, A045917, A234694.
%K A235187 nonn
%O A235187 1,5
%A A235187 _Zhi-Wei Sun_, Jan 04 2014