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

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-------.
            |               |
        .---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

Adjacent sequences: A372027 A372028 A372029 * A372031 A372032 A372033

Keyword

nonn

Author

Rémy Sigrist, Apr 16 2024

Status

approved