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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).
2
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).
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
KEYWORD
nonn,look,base
AUTHOR
Rémy Sigrist, Aug 22 2020
STATUS
approved