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 A270362 #19 Jun 20 2022 20:38:53
%S A270362 0,1,1,2,2,3,3,3,3,4,4,5,5,5,5,5,5,5,5,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,
%T A270362 8,9,9,11,11,11,11,11,11,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,
%U A270362 13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,15,15,18,18,18,18,18,18,18,18,19,19,21,21,21,21,21,21,21,21,21,21,21,21,21,21
%N A270362 Running maxima of Stern's diatomic sequence.
%H A270362 Michael De Vlieger, <a href="/A270362/b270362.txt">Table of n, a(n) for n = 0..10000</a>
%H A270362 Catherine Mary Kenyon, <a href="https://tigerprints.clemson.edu/all_theses/3075">The Calkin-Wilf Tree and Its Various Properties</a>, Master's Thesis, Clemson University (2019), 3075.
%F A270362 a(n) = max_{0 <= i <= n} A002487(i).
%t A270362 FoldList[Max, Nest[Append[#1, If[OddQ[#2], #1[[(#2 + 1)/2]], #1[[#2/2]] + #1[[(#2 + 2)/2]] ]] & @@ {#, Length@ # + 1} &, {0, 1}, 90]] (* _Michael De Vlieger_, Jul 10 2019 *)
%Y A270362 Distinct elements are A212289. Cf. A002487, A212288.
%K A270362 nonn
%O A270362 0,4
%A A270362 _Jeffrey Shallit_, Mar 15 2016