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 A279730 #12 Feb 16 2025 08:33:38
%S A279730 0,0,6,14,34,46,60,60,96,96,118,190,216,216,306,306,340,412,450,450,
%T A279730 492,492,538,538,538,590,590,590,648,948,1010,1010,1010,1078,1078,
%U A279730 1078,1152,1152,1230,1230,1312,1564,1650,1650,1740,1740,1834,1834,1834,1934
%N A279730 Partial sums of A279729.
%H A279730 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A279730 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A279730 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A279730 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%p A279730 with(numtheory): A279730:=n->2*add(add(j * (pi(i)-pi(i-1)) * (pi(2*j-i)-pi(2*j-i-1)) * (product(1-abs((pi(k)-pi(k-1))-(pi(2*j-k)-pi(2*j-k-1))), k=i..j)), i=3..j), j=1..n): seq(A279730(n), n=1..40);
%t A279730 f[n_, x_: 0] := Sum[(If[x == 0, i, 2 n - i] Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]]) Product[1 - Abs[Boole[PrimeQ@ k] - Boole[PrimeQ[2 n - k]]], {k, i, n}], {i, 3, n}]; Accumulate@ Table[f@ n + f[n, 1], {n, 50}] (* _Michael De Vlieger_, Dec 18 2016 *)
%Y A279730 Cf. A278700, A279727, A279728, A279729.
%K A279730 nonn,easy
%O A279730 1,3
%A A279730 _Wesley Ivan Hurt_, Dec 17 2016