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%I #17 Apr 29 2024 09:29:45
%S 0,1,2,4,8,5,16,3,24,6,17,10,32,7,40,12,48,33,64,9,80,14,96,20,65,11,
%T 68,56,128,18,69,19,160,13,66,22,72,15,144,34,84,35,132,49,192,21,130,
%U 41,194,26,36,52,256,25,162,67,260,23,104,37,136,42,272,44
%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of a(n), a(2*n+1) and a(2*n+2) have distinct 1's.
%C This sequence is a permutation of the nonnegative integers with inverse A372131:
%C - for any k >= 0, the first term >= 2^k is precisely 2^k,
%C - all powers of 2 appear in the sequence, in increasing order,
%C - for any v >= 0, every power of 2 that doesn't appear in the binary expansion of v provides an opportunity to select v later, and eventually v will appear in the sequence.
%H Rémy Sigrist, <a href="/A372129/b372129.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A372129/a372129.gp.txt">PARI program</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) AND a(2*n+1) = a(n) AND a(2*n+2) = a(2*n+1) AND a(2*n+2) = 0 for any n >= 0 (where AND denotes the bitwise AND operator).
%e The first terms, arranged alongside a binary tree where siblings have distinct binary 1's and parent and children have distinct binary 1's, are:
%e |
%e .-------0-------.
%e | |
%e .---1---. .---2---.
%e | | | |
%e .-4-. .-8-. .-5-. .16-.
%e | | | | | | | |
%e 3 24 6 17 10 32 7 40
%o (PARI) \\ See Links section.
%Y See A372030 for similar sequences.
%Y Cf. A372130 (analog based on prime factors), A372131 (inverse), A372143 (analog with common 1 bit).
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Apr 20 2024
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