A357523 Reverse run lengths in binary expansions of terms of A166535: for n > 0, a(n) is the unique k such that A166535(k) = A056539(A166535(n)); a(0) = 0.

0, 1, 2, 3, 6, 5, 4, 7, 14, 9, 10, 13, 12, 11, 8, 15, 20, 23, 24, 19, 16, 27, 26, 17, 18, 25, 22, 21, 40, 41, 46, 35, 32, 49, 50, 31, 36, 45, 42, 39, 28, 29, 38, 43, 44, 37, 30, 51, 48, 33, 34, 47, 88, 63, 62, 89, 94, 57, 68, 83, 80, 71, 54, 53, 72, 79, 84, 67

Offset: 0

Author

Rémy Sigrist, Oct 02 2022

Keywords

• nonn
• base

Comments

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

Examples

			For n = 42:
- A166535(42) = 50,
- the binary expansion of 50 is "110010",
- reversing run lengths yields "101100",
- this corresponds to 44 = A166535(38),
- hence a(42) = 38.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..12639
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A357522 for a similar sequence.

Cf. A044918, A056539, A166535.

Programs

PARI

See Links section.

Formula

a(n) = n iff n = 0 or A166535(n) belongs to A044918.