A337304 a(n) is the greatest number m not yet in the sequence such that the binary expansions of n and of m have the same runs of consecutive equal digits (up to order but with multiplicity).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 12, 11, 14, 15, 16, 17, 20, 25, 18, 21, 26, 29, 24, 19, 22, 27, 28, 23, 30, 31, 32, 33, 40, 49, 36, 41, 52, 57, 34, 37, 42, 53, 50, 45, 58, 61, 48, 35, 44, 51, 38, 43, 54, 59, 56, 39, 46, 55, 60, 47, 62, 63, 64, 65, 80, 97

Offset: 0

Author

Rémy Sigrist, Aug 22 2020

Keywords

• nonn
• look
• base

Comments

This sequence has similarities with A337242; here we consider runs, there run lengths.

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

This sequence preserves the Hamming weight (A000120), the number of binary digits (A070939) and the number of runs in binary expansions (A005811).

Examples

			For n = 303:
- the binary expansion of 43 is "100101111",
- the corresponding runs of consecutive equals digits are "1", "00", "1", "0", "1111",
- there are six numbers k with the same multiset of runs:
    k    bin(k)
    ---  -----------
    303  "100101111"
    317  "100111101"
    335  "101001111"
    377  "101111001"
    485  "111100101"
    489  "111101001"
- so a(303) = 489,
     a(317) = 485,
     a(335) = 377,
     a(377) = 335,
     a(485) = 317,
     a(489) = 303.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, PARI program for A337304
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000120, A005811, A070939, A337242.

Programs

PARI

See Links section.

Formula

a(2^k) = 2^k for any k >= 0.

a(2^k-1) = 2^k-1 for any k >= 0.