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 A335993 #8 Aug 03 2020 15:35:40
%S A335993 0,1,2,3,4,6,12,13,16,18,20,24,32,34,44,48,52,54,62,66,70,74,88,94,
%T A335993 108,118,120,132,138,152,158,170,190,216,232,250,252,260,282,290,318,
%U A335993 332,378,384,396,446,450,452,480,481,502,512,526,532,552,592,624,641,674,692,708,728,820,850
%N A335993 High-water marks of the sequence given by the number of twin primes with average n.
%C A335993 Let T(n) be the number of twin primes with average n. These are the high-water marks of the sequence T(n).
%H A335993 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a> (The RECORDS transform returns both the high-water marks and the places where they occur).
%t A335993 m = 10^4; tp = Select[Range[3, m, 2], PrimeQ[#] && Or @@ PrimeQ[# + {-2, 2}] &]; f[n_] := Module[{k = Length @ IntegerPartitions[n, {2}, tp]}, If[MemberQ[tp, n/2], k - 1, k]]; s = {}; fm = 0; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, f1]], {n, 2, m/2, 2}]; Prepend[s, 0] (* _Amiram Eldar_, Jul 11 2020 *)
%Y A335993 The positions at which those high-water marks are attained are given in A335992.
%K A335993 nonn
%O A335993 1,3
%A A335993 _P. Michael Kielstra_, Jul 04 2020