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 A112039 #6 Feb 16 2025 08:32:58
%S A112039 3,9,21,39,65,99,141,191,251,320,396,482,581,686,797,926,1064,1214,
%T A112039 1374,1544,1724,1916,2114,2331,2559,2795,3041,3301,3571,3850,4138,
%U A112039 4447,4762,5096,5444,5800,6170,6551,6944,7349,7769,8201,8642,9095,9557,10030
%N A112039 Let b(0)=1/2, b(n) = b(n-1) + Prime[n]/2; a(n)=b(2*n).
%D A112039 H. L. Nelson, "Prime Sums", J. Rec. Math., 14 (1981), 205-206.
%H A112039 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F A112039 Asymptotically b(n) ~ 2 * n^2 * (log 2 + log(n)). - _Jonathan Vos Post_, Nov 29 2005
%F A112039 b(n) = (1 + A007504(2*n))/2. - _Jonathan Vos Post_, Nov 29 2005
%t A112039 a[0] = 1/2; a[n_] := a[n] = a[n - 1] + Prime[n]/2 bb = Table[a[2*n], {n, 1, 200}]
%Y A112039 Cf. A000040, A007504.
%K A112039 nonn
%O A112039 1,1
%A A112039 _Roger L. Bagula_, Nov 28 2005