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A352726
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have no common runs of consecutive 1's.
2
0, 2, 1, 4, 3, 6, 5, 8, 7, 12, 13, 14, 9, 10, 11, 16, 15, 24, 25, 26, 27, 28, 29, 30, 17, 18, 19, 20, 21, 22, 23, 32, 31, 48, 49, 50, 51, 54, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 33, 34, 35, 36, 38, 39, 37, 40, 41, 42, 43, 44, 45, 46, 47, 64, 63, 96, 97, 98
OFFSET
0,2
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
This sequence has similarities with A238757; here we consider runs of consecutive 1's, there individual 1's in binary expansions.
The binary expansion of n and a(n) may share some 1's, but cannot have a common run of consecutive 1's (as given by A352724).
EXAMPLE
The first terms, alongside the corresponding partitions into runs of 1's, are:
n a(n) runs in n runs in a(n)
-- ---- --------- ------------
0 0 [] []
1 2 [1] [2]
2 1 [2] [1]
3 4 [3] [4]
4 3 [4] [3]
5 6 [1, 4] [6]
6 5 [6] [1, 4]
7 8 [7] [8]
8 7 [8] [7]
9 12 [1, 8] [12]
10 13 [2, 8] [1, 12]
11 14 [3, 8] [14]
12 9 [12] [1, 8]
13 10 [1, 12] [2, 8]
14 11 [14] [3, 8]
15 16 [15] [16]
16 15 [16] [15]
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 30 2022
STATUS
approved