%I #13 Apr 29 2024 09:29:54
%S 0,1,3,5,2,6,4,7,10,11,12,13,14,15,9,17,8,24,18,19,20,21,22,23,25,26,
%T 27,28,29,30,16,31,40,41,42,43,34,35,33,37,36,38,39,44,45,46,47,49,48,
%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,65,32,96,67,69
%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, the binary expansions of a(n), a(2*n) and a(2*n+1) have a common 1 bit.
%C Conjecture: this sequence is a permutation of the nonnegative integers.
%H Rémy Sigrist, <a href="/A372143/b372143.txt">Table of n, a(n) for n = 0..9999</a>
%H Rémy Sigrist, <a href="/A372143/a372143.gp.txt">PARI program</a>
%F a(n) AND a(2*n) AND a(2*n+1) <> 0 for any n > 0 (where AND denotes the bitwise AND operator).
%e The first terms, arranged alongside a binary tree where each parent node (except the root) and its children share some 1 bit, are:
%e |
%e 0
%e |
%e .-------1-------.
%e | |
%e .---3---. .---5---.
%e | | | |
%e .-2-. .-6-. .-4-. .-7-.
%e | | | | | | | |
%e 10 11 12 13 14 15 9 17
%o (PARI) \\ See Links section.
%Y See A372030 for similar sequences.
%Y Cf. A372129 (analog without common 1 bit).
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Apr 20 2024