|
| |
|
|
A372143
|
|
Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, the binary expansions of a(n), a(2*n) and a(2*n+1) have a common 1 bit.
|
|
4
|
|
|
|
0, 1, 3, 5, 2, 6, 4, 7, 10, 11, 12, 13, 14, 15, 9, 17, 8, 24, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 16, 31, 40, 41, 42, 43, 34, 35, 33, 37, 36, 38, 39, 44, 45, 46, 47, 49, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 32, 96, 67, 69
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Conjecture: this sequence is a permutation of the nonnegative integers.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) AND a(2*n) AND a(2*n+1) <> 0 for any n > 0 (where AND denotes the bitwise AND operator).
|
|
|
EXAMPLE
|
The first terms, arranged alongside a binary tree where each parent node (except the root) and its children share some 1 bit, are:
|
0
|
.-------1-------.
| |
.---3---. .---5---.
| | | |
.-2-. .-6-. .-4-. .-7-.
| | | | | | | |
10 11 12 13 14 15 9 17
|
|
|
PROG
|
(PARI) \\ See Links section.
|
|
|
CROSSREFS
|
Cf. A372129 (analog without common 1 bit).
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
