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 A305125 #21 May 27 2018 21:13:27
%S A305125 0,1,2,2,4,6,3,3,10,8,8,17,9,11,27,11,12,27,14,21,39,17,19,36,28,22,
%T A305125 48,25,24,75,30,25,68,35,56,68,37,40,93,54,43,103,42,52,125,51,49,117,
%U A305125 64,76,130,63,56,135,99,78,151,76,73,198
%N A305125 Number of ways to express n^2 as average of two primes p1 < p2.
%H A305125 Hugo Pfoertner, <a href="/A305125/b305125.txt">Table of n, a(n) for n = 1..10000</a>
%F A305125 a(n) = A002375(n^2).
%t A305125 f[n_]:=Length[Select[2 n - Prime[Range[2, PrimePi[n]]], PrimeQ]]; Table[f[n^2], {n, 60}] (* _Vincenzo Librandi_, May 26 2018 *)
%o A305125 (PARI) for (n=1,60,k=0;n2=2*n*n;forprime(p=3,n2/2,if(isprime(n2-p),k++));print1(k,", "))
%Y A305125 Cf. A002375, A172989, A304874, A304875, A304903, A304904, A304905, A305126.
%K A305125 nonn,look
%O A305125 1,3
%A A305125 _Hugo Pfoertner_, May 26 2018