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 A238585 #7 Mar 01 2014 11:55:45
%S A238585 0,0,0,1,1,0,1,2,2,1,1,1,3,2,3,2,2,3,1,5,1,1,3,2,4,5,2,4,3,4,1,4,5,3,
%T A238585 4,6,3,2,2,2,2,1,8,1,3,4,7,2,5,3,2,2,4,7,4,3,2,3,5,7,5,3,6,6,5,3,4,5,
%U A238585 2,2,2,3,7,2,3,7,3,4,10,3
%N A238585 Number of primes p < n with prime(p)^2 + (prime(n)-1)^2 prime.
%C A238585 Conjecture: (i) a(n) > 0 unless n divides 6, and a(n) = 1 only for n = 4, 5, 7, 10, 11, 12, 19, 21, 22, 31, 42, 44.
%C A238585 (ii) If n > 2 is not equal to 9, then prime(n)^2 + (prime(p) - 1)^2 is prime for some prime p < n.
%C A238585 (iii) For n > 3, there is a prime p < n with prime(p) + prime(n) + 1 prime. If n > 9 is not equal to 18, then prime(p)^2 + prime(n)^2 - 1 is prime for some prime p < n.
%H A238585 Zhi-Wei Sun, <a href="/A238585/b238585.txt">Table of n, a(n) for n = 1..10000</a>
%H A238585 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014.
%e A238585 a(7) = 1 since 3 and prime(3)^2 + (prime(7)-1)^2 = 5^2 + 16^2 = 281 are both prime.
%e A238585 a(44) = 1 since 23 and prime(23)^2 + (prime(44)-1)^2 = 83^2 + 192^2 = 43753 are both prime.
%t A238585 p[n_,k_]:=PrimeQ[k]&&PrimeQ[Prime[k]^2+(Prime[n]-1)^2]
%t A238585 a[n_]:=Sum[If[p[n,k],1,0],{k,1,n-1}]
%t A238585 Table[a[n],{n,1,80}]
%Y A238585 Cf. A000040, A232465, A238580.
%K A238585 nonn
%O A238585 1,8
%A A238585 _Zhi-Wei Sun_, Mar 01 2014