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

0,3

Comments

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

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

Formula

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

See A357523 for a similar sequence.

Cf. A044918, A056539, A063037.

Sequence in context: A056023 A133259 A120067 * A089843 A269378 A131145

Adjacent sequences: A357519 A357520 A357521 * A357523 A357524 A357525

Keyword

nonn,look,base

Author

Rémy Sigrist, Oct 02 2022

Status

approved