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 A236472 #10 Jan 19 2019 04:14:59
%S A236472 0,1,1,0,1,2,2,2,2,1,2,1,2,1,0,1,1,2,3,0,1,1,1,2,0,1,1,0,0,2,0,2,2,1,
%T A236472 0,0,3,1,2,0,2,2,2,1,0,0,4,1,0,0,0,0,5,0,1,1,1,2,1,1,3,0,0,2,2,0,2,2,
%U A236472 2,3,1,1,2,1,1,2,2,3,3,3,2,0,0,2,1,1,3,0,0,2,0,3,0,0,1,1,0,2,0,0
%N A236472 a(n) = |{0 < k < n: p = prime(k) + phi(n-k), prime(p) + 2 and prime(p) + 6 are all prime}|, where phi(.) is Euler's totient function.
%C A236472 Conjecture: a(n) > 0 for every n = 330, 331, ....
%C A236472 We have verified this for n up to 80000.
%C A236472 The conjecture implies that there are infinitely many prime triples of the form {prime(p), prime(p) + 2, prime(p) + 6} with p prime. See A236464 for such primes p.
%H A236472 Zhi-Wei Sun, <a href="/A236472/b236472.txt">Table of n, a(n) for n = 1..10000</a>
%e A236472 a(10) = 1 since prime(2) + phi(8) = 3 + 4 = 7, prime(7) + 2 = 17 + 2 = 19 and prime(7) + 6 = 23 are all prime.
%e A236472 a(877) = 1 since prime(784) + phi(877-784) = 6007 + 60 = 6067, prime(6067) + 2 = 60101 + 2 = 60103 and prime(6067) + 6 = 60107 are all prime.
%t A236472 p[n_]:=PrimeQ[n]&&PrimeQ[Prime[n]+2]&&PrimeQ[Prime[n]+6]
%t A236472 f[n_,k_]:=Prime[k]+EulerPhi[n-k]
%t A236472 a[n_]:=Sum[If[p[f[n,k]],1,0],{k,1,n-1}]
%t A236472 Table[a[n],{n,1,100}]
%Y A236472 Cf. A000010, A000040, A022004, A236456, A236460, A236464, A236467, A236470.
%K A236472 nonn
%O A236472 1,6
%A A236472 _Zhi-Wei Sun_, Jan 26 2014