A372128 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(2*n+1) = a(2*n) OR a(n) (where OR denotes the bitwise OR operator).

1, 2, 3, 4, 6, 5, 7, 8, 12, 9, 15, 16, 21, 17, 23, 18, 26, 10, 14, 19, 27, 20, 31, 13, 29, 32, 53, 24, 25, 33, 55, 28, 30, 34, 58, 35, 43, 36, 46, 40, 59, 37, 63, 38, 54, 64, 95, 39, 47, 41, 61, 65, 97, 66, 119, 44, 60, 48, 57, 50, 51, 72, 127, 42, 62, 68, 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

Example

The first terms, arranged alongside a binary tree where each right child equals its parent OR its sibling, are:
                |
        .-------1-------.
        |               |
    .---2---.       .---3---.
    |       |       |       |
  .-4-.   .-6-.   .-5-.   .-7-.
  |   |   |   |   |   |   |   |
  8  12   9  15  16  21  17  23

Prog

(PARI) \\ See Links section.

Crossrefs

See A372030 for similar sequences.

Cf. A372032 (analog for bitwise XOR operator).

Sequence in context: A072758 A104464 A352725 * A367307 A139706 A333777

Adjacent sequences: A372125 A372126 A372127 * A372129 A372130 A372131

Keyword

nonn,base

Author

Rémy Sigrist, Apr 20 2024

Status

approved