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A352728
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have exactly one common run of consecutive 1's.
1
1, 2, 3, 4, 9, 6, 7, 8, 5, 11, 10, 12, 17, 14, 15, 16, 13, 19, 18, 22, 23, 20, 21, 24, 26, 25, 35, 28, 33, 30, 31, 32, 29, 36, 27, 34, 38, 37, 40, 39, 44, 45, 46, 41, 42, 43, 79, 48, 50, 49, 52, 51, 54, 53, 71, 56, 58, 57, 67, 60, 65, 62, 63, 64, 61, 68, 59
OFFSET
1,2
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
This sequence is a variant of A238758; here we consider runs of consecutive 1's, there individual 1's in binary expansions.
We only consider runs of consecutive 1's that completely match in binary expansions of n and a(n), not simply single common 1's.
EXAMPLE
The first terms, alongside the corresponding runs of 1's in binary expansions, are:
n a(n) runs in n runs in a(n)
-- ---- --------- ------------
1 1 [1] [1]
2 2 [2] [2]
3 3 [3] [3]
4 4 [4] [4]
5 9 [1, 4] [1, 8]
6 6 [6] [6]
7 7 [7] [7]
8 8 [8] [8]
9 5 [1, 8] [1, 4]
10 11 [2, 8] [3, 8]
11 10 [3, 8] [2, 8]
12 12 [12] [12]
13 17 [1, 12] [1, 16]
14 14 [14] [14]
15 15 [15] [15]
16 16 [16] [16]
PROG
(PARI) See Links section.
CROSSREFS
Sequence in context: A356886 A359416 A222248 * A236852 A363318 A236837
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 30 2022
STATUS
approved