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%I #16 Apr 29 2024 09:29:33
%S 1,2,3,4,6,5,8,7,11,9,15,12,17,10,18,13,20,14,25,19,28,16,31,21,33,22,
%T 39,24,34,23,41,27,40,26,46,29,43,30,55,32,51,35,63,36,52,37,68,38,59,
%U 42,75,44,66,45,84,47,71,48,82,49,72,50,91,53,80,54,94
%N Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(2*n+1) = a(2*n) + a(n).
%C Conjecture: this sequence is a permutation of the positive integers.
%H Rémy Sigrist, <a href="/A372030/b372030.txt">Table of n, a(n) for n = 1..10001</a>
%H Rémy Sigrist, <a href="/A372030/a372030.gp.txt">PARI program</a>
%H Rémy Sigrist, <a href="/A372030/a372030.png">Colored scatterplot of the first 100000 terms</a> (where the color is function of the 2-adic valuation of n+1)
%e The first terms, arranged alongside a binary tree where each right child equals its parent plus its sibling, are:
%e |
%e .-------1-------.
%e | |
%e .---2---. .---3---.
%e | | | |
%e .-4-. .-6-. .-5-. .-8-.
%e | | | | | | | |
%e 7 11 9 15 12 17 10 18
%o (PARI) \\ See Links section.
%Y See A372031, A372032, A372127, A372128, A372129, A372130, A372143 and A372144 for similar sequences.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Apr 16 2024