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A372659
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the Fibonacci numbers that appear in the Zeckendorf representation of n do not appear in the dual Zeckendorf representation of a(n).
3
0, 2, 1, 3, 20, 4, 15, 12, 5, 7, 13, 8, 29, 6, 10, 21, 16, 36, 9, 19, 63, 11, 18, 17, 28, 33, 14, 26, 59, 22, 54, 56, 57, 101, 23, 34, 25, 27, 96, 46, 53, 88, 24, 44, 51, 42, 211, 38, 49, 93, 92, 180, 47, 91, 207, 30, 37, 64, 50, 62, 43, 60, 80, 31, 41, 85, 76
OFFSET
0,2
COMMENTS
The dual Zeckendorf representation is also known as the lazy Fibonacci representation (see A356771 for further details).
This sequence is a permutation of the nonnegative integers with inverse A372660.
EXAMPLE
The first terms, alongside the Zeckendorf representation of n and the dual Zeckendorf representation of a(n), in binary, are:
n a(n) z(n) d(a(n))
-- ---- ------ --------
0 0 0 0
1 2 1 10
2 1 10 1
3 3 100 10
4 20 101 101010
5 4 1000 101
6 15 1001 110110
7 12 1010 10101
8 5 10000 111
9 7 10001 1110
10 13 10010 101101
11 8 10100 1011
12 29 10101 10101010
PROG
(PARI) \\ See Links section.
CROSSREFS
See A372657 for a similar sequence.
Cf. A356771, A372660 (inverse).
Sequence in context: A156364 A106169 A319493 * A340202 A108353 A337894
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 09 2024
STATUS
approved