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A371343
Lexicographically latest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and of a(n) have the same length (A070939) and the same number of runs of consecutive equals digits (A005811).
1
0, 1, 2, 3, 6, 5, 4, 7, 14, 13, 10, 11, 12, 9, 8, 15, 30, 29, 26, 27, 22, 21, 20, 25, 28, 23, 18, 19, 24, 17, 16, 31, 62, 61, 58, 59, 54, 53, 52, 57, 50, 45, 42, 43, 46, 41, 44, 55, 60, 51, 40, 49, 38, 37, 36, 47, 56, 39, 34, 35, 48, 33, 32, 63, 126, 125, 122
OFFSET
0,3
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers with infinitely many fixed points (for example, all terms of A000225 are fixed points).
EXAMPLE
The first terms, in decimal and in binary, are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0
1 1 1 1
2 2 10 10
3 3 11 11
4 6 100 110
5 5 101 101
6 4 110 100
7 7 111 111
8 14 1000 1110
9 13 1001 1101
10 10 1010 1010
11 11 1011 1011
12 12 1100 1100
13 9 1101 1001
14 8 1110 1000
15 15 1111 1111
PROG
(PARI) \\ See Links section.
CROSSREFS
See A331274 and A337242 for similar sequences.
Sequence in context: A175949 A166404 A337242 * A166166 A106452 A254118
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 24 2024
STATUS
approved