A357527 Reverse run lengths in binary expansions of terms of A044813: for n > 0, a(n) is the unique k such that A044813(k) = A056539(A044813(n)); a(0) = 0.

0, 1, 2, 4, 3, 5, 7, 6, 8, 12, 11, 10, 9, 13, 23, 18, 20, 22, 15, 21, 16, 19, 17, 14, 24, 36, 29, 33, 35, 26, 34, 32, 31, 27, 30, 28, 25, 37, 55, 44, 47, 49, 52, 54, 39, 53, 51, 40, 50, 41, 48, 46, 42, 45, 43, 38, 56, 82, 63, 68, 76, 79, 81, 58, 69, 73, 80, 78

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:
- A044813(42) = 159,
- the binary expansion of 159 is "10011111",
- reversing run lengths yields "11111001",
- this corresponds to 249 = A044813(52),
- hence a(42) = 52.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..11666
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A057164, A357522 and A357523 for similar sequences.

Cf. A044813, A044918, A056539.

Programs

PARI

See Links section.

Formula

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