A357530 Reverse run lengths in binary expansions of terms of A031443: for n > 0, a(n) is the unique k such that A031443(k) = A056539(A031443(n)); a(0) = 0.

0, 1, 2, 3, 4, 11, 8, 7, 6, 9, 12, 5, 10, 13, 14, 45, 41, 31, 18, 38, 28, 21, 22, 27, 37, 36, 26, 23, 20, 29, 39, 17, 32, 42, 46, 35, 25, 24, 19, 30, 40, 16, 33, 43, 47, 15, 34, 44, 48, 49, 170, 165, 150, 115, 54, 161, 146, 111, 58, 136, 101, 68, 81, 88, 123

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:
- A031443(42) = 210,
- the binary expansion of 210 is "11010010",
- reversing run lengths yields "10110100",
- this corresponds to 180 = A031443(33),
- hence a(42) = 33.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8788
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A057164 for a similar sequence.

Cf. A031443, A044918, A056539.

Programs

PARI

See Links section.

Formula

a(n) = n iff n = 0 or A031443(n) belongs to A044918.