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Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(2*n+1) = a(2*n) + a(n).
9

%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