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 A262730 #20 May 31 2018 03:47:37
%S A262730 2,3,23,83,199,331,487,1069,1289,1697,2467,3463,3617,3733,5153,5449,
%T A262730 6221,9203,9811,9967,12473,13883,14723,15791,16001,18919,33589,33827,
%U A262730 46093,58321,59051,59921,60289,71249,84349,85133,88211,124309,126047,126359,127541,145679,146807,153247,165233
%N A262730 Primes p such that p^2 = pi(x^3) + pi(y^3) for some positive integers x and y, where pi(m) denotes the number of primes not exceeding m.
%C A262730 Conjecture: (i) The sequence has infinitely many terms.
%C A262730 (ii) There are infinitely many primes p such that p^2 = pi(x^3+y^3) for some positive integers x and y.
%C A262730 See also A262731 for a related conjecture.
%D A262730 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 A262730 Chai Wah Wu, <a href="/A262730/b262730.txt">Table of n, a(n) for n = 1..132</a>
%H A262730 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 A262730 a(1) = 2 since pi(1^3)+pi(2^3) = 0+4 = 2^2 with 2 prime.
%e A262730 a(3) = 23 since pi(9^3)+pi(14^3) = pi(729)+pi(2744) = 129+400 = 529 = 23^2 with 23 prime.
%e A262730 a(20) = 9967 since pi(841^3)+pi(1109^3) = pi(594823321)+pi(1363938029) = 31068537+68272552 = 99341089 = 9967^2 with 9967 prime.
%e A262730 a(38) = 124309 since pi(5773^3)+pi(5779^3) = pi(192399824917)+pi(193000344139) = 7714808769+7737918712 = 15452727481 = 124309^2 with 124309 prime.
%e A262730 a(45) = 165233 since pi(6924^3)+pi(7148^3) = pi(331948857024)+pi(365219225792) = 13025048890+14276895399 = 27301944289 = 165233^2 with 165233 prime.
%t A262730 f[n_]:=PrimePi[n^3]
%t A262730 T[1]:={0}
%t A262730 T[n_]:=Union[T[n-1],{f[n]}]
%t A262730 n=0;Do[Do[If[f[x]>Prime[y]^2,Goto[aa]];If[MemberQ[T[Prime[y]],Prime[y]^2-f[x]],n=n+1;Print[n," ",Prime[y]];Goto[aa]];Continue,{x,1,Prime[y]}];
%t A262730 Label[aa];Continue,{y,1,15111}]
%Y A262730 Cf. A000040, A000290, A000578, A000720, A262409, A262462, A262536, A262698, A262722, A262731.
%K A262730 nonn,hard
%O A262730 1,1
%A A262730 _Zhi-Wei Sun_, Sep 28 2015