A357522 Reverse run lengths in binary expansions of terms of A063037: for n >= 0, a(n) is the unique k such that A063037(1+k) = A056539(A063037(1+n)).

0, 1, 2, 3, 6, 5, 4, 7, 8, 11, 10, 9, 16, 17, 18, 15, 12, 13, 14, 19, 32, 23, 22, 21, 24, 31, 28, 27, 26, 29, 30, 25, 20, 33, 42, 49, 48, 43, 44, 47, 50, 41, 34, 37, 38, 53, 52, 39, 36, 35, 40, 51, 46, 45, 74, 75, 84, 65, 58, 59, 64, 85, 86, 63, 60, 57, 66, 83

Offset: 0

Author

Rémy Sigrist, Oct 02 2022

Keywords

• nonn
• look
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

Examples

			For n = 42:
- A063037(1+42) = 86,
- the binary expansion of 86 is "1010110",
- reversing run lengths yields "1001010",
- this corresponds to 74 = A063037(1+34),
- hence a(42) = 34.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10944
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A357523 for a similar sequence.

Cf. A044918, A056539, A063037.

Programs

PARI

See Links section.

Formula

a(n) = n iff n = 0 or A044813(1+n) belongs to A044918.