A366062 Lexicographically earliest infinite sequence of distinct nonnegative integers such that for any k > 0, the k-th binary digit in the even bisection is different from the k-th binary digit in the odd bisection.

0, 2, 4, 1, 3, 8, 5, 9, 16, 14, 10, 20, 6, 11, 17, 18, 21, 19, 32, 28, 12, 13, 33, 56, 24, 29, 34, 26, 22, 36, 25, 48, 57, 49, 50, 40, 58, 41, 51, 35, 64, 7, 15, 65, 37, 80, 59, 66, 52, 27, 67, 96, 112, 30, 23, 128, 60, 53, 81, 97, 113, 98, 104, 114, 105, 99

Offset

0,2

Comments

Leading zeros in binary expansions of positive values are ignored.

Is this sequence a permutation of the nonnegative integers?

Links

Table of n, a(n) for n=0..65.

Rémy Sigrist, PARI program

Example

The even and odd bisections, in decimal and in binary, begin as follows:
a(2n)        |0|  4  | 3 |  5  |   16    |  10   |  6  |   17    |   21    |...
bin(a(2n))   |0|1 0 0|1 1|1 0 1|1 0 0 0 0|1 0 1 0|1 1 0|1 0 0 0 1|1 0 1 0 1|...
bin(a(2n+1)) |1 0|1|1 0 0 0|1 0 0 1|1 1 1 0|1 0 1 0 0|1 0 1 1|1 0 0 1 0|...
a(2n+1)      | 2 |1|   8   |   9   |  14   |   20    |  11   |   18    |...

Prog

(PARI) See Links section.

Crossrefs

Cf. A333010.

Sequence in context: A290824 A272977 A230505 * A208526 A275895 A369292

Adjacent sequences: A366059 A366060 A366061 * A366063 A366064 A366065

Keyword

nonn,base

Author

Rémy Sigrist, Sep 27 2023

Status

approved