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

0,3

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).

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

Formula

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

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000120, A005811, A070939, A337242.

Sequence in context: A322464 A057889 A235027 * A325402 A110029 A302027

Adjacent sequences: A337301 A337302 A337303 * A337305 A337306 A337307

Keyword

nonn,look,base

Author

Rémy Sigrist, Aug 22 2020

Status

approved