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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).
3
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, 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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 16 2024
STATUS
approved