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 A258141 #11 May 22 2015 03:48:52
%S A258141 0,0,0,0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,2,1,0,1,0,1,1,0,
%T A258141 1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,2,1,0,2,0,2,1,0,0,1,0,2,1,0,1,2,0,2,
%U A258141 0,0,1,2,0,0,1,0,1,2,0,1,0,0,1,1,0,2,1,0,0,1,0,2,1,0,0,2,0,1,0,0
%N A258141 Number of ways to write n as p^2 + q with p, q and 2*p + 3 all prime.
%C A258141 Conjecture: For any integer n > 0, we have a(n+r) > 0 for some r = 0,1,2,3,4,5.
%C A258141 We have verified this for n up to 10^8. See also A258139 for a weaker version of this conjecture.
%C A258141 The conjecture is somewhat similar to Goldbach's Conjecture. It implies that there are infinitely many primes p with 2*p + 3 prime.
%H A258141 Zhi-Wei Sun, <a href="/A258141/b258141.txt">Table of n, a(n) for n = 1..10000</a>
%e A258141 a(11) = 1 since 11 = 2^2 + 7 with 2, 7 and 2*2 + 3 all prime.
%t A258141 Do[r=0;Do[If[PrimeQ[2Prime[k]+3]&&PrimeQ[n-Prime[k]^2],r=r+1],{k,1,PrimePi[Sqrt[n]]}];Print[n," ",r];Continue,{n,1,100}]
%Y A258141 Cf. A000040, A002375, A023204, A258139, A258140.
%K A258141 nonn
%O A258141 1,27
%A A258141 _Zhi-Wei Sun_, May 22 2015