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 A361144 #17 Mar 07 2023 07:42:28
%S A361144 1,2,4,5,6,7,8,10,11,14,15,17,16,19,20,21,22,23,24,26,27,28,29,30,33,
%T A361144 34,36,37,38,39,40,42,44,46,47,49,48,51,52,53,54,56,58,60,61,62,63,64,
%U A361144 65,66,68,69,70,71,72,74,75,78,79,81,80,83,84,85,86,87,88
%N A361144 Lexicographically earliest sequence of positive integers such that the sums Sum_{i = 1+k*2^e..(k+1)*2^e} a(i) with k, e >= 0 are all distinct.
%C A361144 In other words, a(1), a(2), a(1)+a(2), a(3), a(4), a(3)+a(4), a(1)+a(2)+a(3)+a(4), a(5), a(6), a(5)+a(6), etc. are all distinct (see A361227 for these values).
%C A361144 In particular, all terms are distinct (but not necessarily in increasing order).
%C A361144 We can arrange the terms of the sequence as the leaves of a perfect infinite binary tree, the sums with e > 0 corresponding to parent nodes; each node will contain a different value and all values will appear in the tree (if n = 2^m+1 for some m > 0, then a(n) will equal the least missing value so far in the tree).
%H A361144 Rémy Sigrist, <a href="/A361144/a361144.gp.txt">PARI program</a>
%H A361144 Rémy Sigrist, <a href="/A361144/a361144.txt">C++ program</a>
%F A361144 Empirically, a(n) ~ 4*n/3 as n tends to infinity.
%e A361144 The first terms (at the bottom of the tree) alongside the corresponding sums are:
%e A361144 176
%e A361144 ---------------------------------
%e A361144 43 133
%e A361144 ----------------- -----------------
%e A361144 12 31 57 76
%e A361144 --------- --------- --------- ---------
%e A361144 3 9 13 18 25 32 35 41
%e A361144 ----- ----- ----- ----- ----- ----- ----- -----
%e A361144 1 2 4 5 6 7 8 10 11 14 15 17 16 19 20 21
%o A361144 (PARI) See Links section.
%o A361144 (C++) See Links section.
%Y A361144 See A360305, A361189, A361191 and A361234 for other variants.
%Y A361144 Cf. A326936, A361146, A361227.
%K A361144 nonn
%O A361144 1,2
%A A361144 _Rémy Sigrist_, Mar 02 2023