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 A026138 #17 Aug 28 2021 02:53:23
%S A026138 1,2,4,5,8,10,11,13,14,17,20,22,23,26,28,29,31,32,35,37,38,40,41,44,
%T A026138 47,49,50,53,56,58,59,62,64,65,67,68,71,74,76,77,80,82,83,85,86,89,91,
%U A026138 92,94,95,98,101,103,104,107,109,110,112,113
%N A026138 Numbers k such that s(j) < s(k) for all j < k, where s = A026136.
%C A026138 Also a(n) = (1/2)*s(n+1), where s = A026169.
%C A026138 That these definitions produce the same sequence can be established using the methods in the Dekking paper.
%C A026138 Indices of records in A026136. - _Michael De Vlieger_, Aug 27 2021
%H A026138 Michael De Vlieger, <a href="/A026138/b026138.txt">Table of n, a(n) for n = 1..10000</a>
%H A026138 F. M. Dekking, <a href="https://arxiv.org/abs/2001.08915">Permutations of N generated by left-right filling algorithms</a>, arXiv:2001.08915 [math.CO], 2020.
%t A026138 Block[{a, r, s, nn = 113}, a[1] = 1; Do[If[! IntegerQ[a[#1]], Set[a[#1], i], Set[a[#2], i]] & @@ {i - #, i + #} &@ Floor[i/2], {i, 2 nn}]; s = TakeWhile[Array[a[#] &, nn], IntegerQ]; Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Aug 27 2021 *)
%Y A026138 Cf. A026136, A026139 (records in A026136), A026169.
%K A026138 nonn
%O A026138 1,2
%A A026138 _Clark Kimberling_
%E A026138 Edited by _N. J. A. Sloane_, Jan 31 2020