A372032 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(2*n+1) = a(2*n) XOR a(n) (where XOR denotes the bitwise XOR operator).

1, 2, 3, 4, 6, 8, 11, 9, 13, 10, 12, 7, 15, 5, 14, 16, 25, 17, 28, 18, 24, 19, 31, 26, 29, 20, 27, 32, 37, 33, 47, 34, 50, 35, 58, 36, 53, 39, 59, 38, 52, 40, 48, 42, 57, 41, 54, 43, 49, 46, 51, 44, 56, 64, 91, 23, 55, 65, 100, 30, 63, 66, 109, 67, 97, 68, 118

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 XOR its sibling, are:
                    |
            .-------1-------.
            |               |
        .---2---.       .---3---.
        |       |       |       |
      .-4-.   .-6-.   .-8-.   .11-.
      |   |   |   |   |   |   |   |
      9  13  10  12   7  15   5  14

Prog

(PARI) \\ See Links section.

Crossrefs

See A372030 for similar sequences.

Cf. A372128 (analog for bitwise OR operator).

Sequence in context: A247334 A237450 A165514 * A182417 A189704 A223543

Adjacent sequences: A372029 A372030 A372031 * A372033 A372034 A372035

Keyword

nonn,base

Author

Rémy Sigrist, Apr 16 2024

Status

approved