A372030 - OEIS

A372030

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

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, 39, 24, 34, 23, 41, 27, 40, 26, 46, 29, 43, 30, 55, 32, 51, 35, 63, 36, 52, 37, 68, 38, 59, 42, 75, 44, 66, 45, 84, 47, 71, 48, 82, 49, 72, 50, 91, 53, 80, 54, 94

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Conjecture: this sequence is a permutation of the positive integers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10001

Rémy Sigrist, PARI program

Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of the 2-adic valuation of n+1)

EXAMPLE

The first terms, arranged alongside a binary tree where each right child equals its parent plus its sibling, are:

.-------1-------.