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 A236358 #6 Jan 23 2014 09:50:17
%S A236358 0,0,0,0,0,0,0,1,1,1,1,0,0,0,1,2,1,0,2,3,1,1,0,2,1,0,2,3,3,3,2,3,2,1,
%T A236358 4,1,4,1,4,5,3,5,7,7,8,5,5,4,4,7,7,4,7,3,6,4,5,5,6,7,6,4,5,7,6,9,5,8,
%U A236358 7,7,4,6,5,4,6,9,8,3,6,8,9,8,8,7,8,8,9,8,4,7,4,7,7,5,4,8,6,6,7,11
%N A236358 a(n) = |{0 < k < n: m = phi(k)/2 + phi(n-k)/12 is an integer with 2*3^m + 1 prime}|, where phi(.) is Euler's totient function.
%C A236358 Conjecture: (i) a(n) > 0 for all n > 26.
%C A236358 (ii) For any integer n > 37, there is a positive integer k < n such that m = phi(k)/2 + phi(n-k)/12 is an integer with 2*3^m - 1 prime.
%C A236358 We have verified both parts for n up to 50000. Clearly, part (i) implies that there are infinitely many positive integers m with 2*3^m + 1 prime, while part (ii) implies that there are infinitely many positive integers m with 2*3^m - 1 prime.
%H A236358 Zhi-Wei Sun, <a href="/A236358/b236358.txt">Table of n, a(n) for n = 1..10000</a>
%e A236358 a(36) = 1 since phi(15)/2 + phi(21)/12 = 4 + 1 = 5 with 2*3^5 + 1 = 487 prime.
%t A236358 p[n_]:=IntegerQ[n]&&PrimeQ[2*3^n+1]
%t A236358 f[n_,k_]:=EulerPhi[k]/2+EulerPhi[n-k]/12
%t A236358 a[n_]:=Sum[If[p[f[n,k]],1,0],{k,1,n-1}]
%t A236358 Table[a[n],{n,1,100}]
%Y A236358 Cf. A000010, A000040, A000244, A079363, A111974, A234451, A234503, A234504.
%K A236358 nonn
%O A236358 1,16
%A A236358 _Zhi-Wei Sun_, Jan 23 2014