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

Author

Rémy Sigrist, Sep 27 2023

Keywords

• nonn
• base

Comments

Leading zeros in binary expansions of positive values are ignored.

Is this sequence a permutation of the nonnegative integers?

Examples

			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    |...
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A333010.

Programs

PARI

See Links section.