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A372030
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(2*n+1) = a(2*n) + a(n).
9
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
OFFSET
1,2
COMMENTS
Conjecture: this sequence is a permutation of the positive integers.
LINKS
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-------.
| |
.---2---. .---3---.
| | | |
.-4-. .-6-. .-5-. .-8-.
| | | | | | | |
7 11 9 15 12 17 10 18
PROG
(PARI) \\ See Links section.
CROSSREFS
See A372031, A372032, A372127, A372128, A372129, A372130, A372143 and A372144 for similar sequences.
Sequence in context: A285041 A265734 A299759 * A232560 A183090 A232559
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 16 2024
STATUS
approved