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 A261515 #14 Jun 18 2017 12:07:07
%S A261515 5,17,59,71,103,157,353,787,4567,4621,6857,63317,124769,336773,
%T A261515 14178581,37187119,214544387,214811057,215602631,271249247,273928639,
%U A261515 431274143,544625929,851377883,3913864351,5964539507,5964539519,11097645023,11097974947,11102342221,45063304271,142799017567,207890420203,207913758571
%N A261515 Primes of the form p(q) + p(r) with q and r both prime, where p(.) is the partition function given by A000041.
%C A261515 The conjecture in A261513 implies that the current sequence has infinitely many terms.
%D A261515 Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.
%H A261515 Zhi-Wei Sun, <a href="/A261515/b261515.txt">Table of n, a(n) for n = 1..10000</a>
%H A261515 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641 [math.NT], 2014.
%e A261515 a(1) = 5 since p(2) + p(3) = 2 + 3 = 5 with 2, 3 and 5 all prime.
%e A261515 a(2) = 17 since p(2) + p(7) = 2 + 15 = 17 with 2, 7 and 17 all prime.
%t A261515 f[n_]:=PartitionsP[Prime[n]]
%t A261515 n=0;Do[If[PrimeQ[f[k]+f[m]],n=n+1;Print[n," ",f[k]+f[m]]],{m,1,40},{k,1,m}]
%Y A261515 Cf. A000040, A000041, A259678, A261513.
%K A261515 nonn
%O A261515 1,1
%A A261515 _Zhi-Wei Sun_, Aug 22 2015