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A338698
Lexicographically latest sequence of distinct nonnegative terms such that for any n >= 0, n and a(n) have the same number of 0's and the same number of 1's in their Zeckendorf-binary representations.
1
0, 1, 2, 3, 4, 5, 7, 6, 8, 11, 10, 9, 12, 13, 18, 16, 15, 20, 14, 19, 17, 21, 29, 26, 24, 32, 23, 31, 30, 22, 28, 27, 25, 33, 34, 47, 42, 39, 52, 37, 50, 49, 36, 48, 45, 44, 54, 35, 43, 41, 40, 53, 38, 51, 46, 55, 76, 68, 63, 84, 60, 81, 79, 58, 78, 77, 73, 87
OFFSET
0,3
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
FORMULA
A007895(a(n)) = A007895(n).
A072649(a(n)) = A072649(n) for any n > 0.
a(A000045(n)) = A000045(n).
EXAMPLE
The first terms, alongside their Zeckendorf-binary representation, are:
n a(n) zeck(n) zeck(a(n))
-- ---- ------- ----------
0 0 0 0
1 1 1 1
2 2 10 10
3 3 100 100
4 4 101 101
5 5 1000 1000
6 7 1001 1010
7 6 1010 1001
8 8 10000 10000
9 11 10001 10100
10 10 10010 10010
11 9 10100 10001
12 12 10101 10101
13 13 100000 100000
14 18 100001 101000
15 16 100010 100100
16 15 100100 100010
17 20 100101 101010
18 14 101000 100001
19 19 101001 101001
20 17 101010 100101
PROG
(PARI) See Links section.
CROSSREFS
Cf. A000045, A007895, A072649, A014417, A331274 (binary variant).
Sequence in context: A056017 A091995 A343150 * A361946 A066937 A217266
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 24 2021
STATUS
approved