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A372654
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the dual Zeckendorf representations of n and a(n) have no common missing Fibonacci number.
2
0, 1, 3, 2, 5, 4, 6, 9, 10, 7, 8, 11, 15, 16, 17, 12, 13, 14, 19, 18, 25, 26, 27, 29, 28, 20, 21, 22, 24, 23, 31, 30, 32, 41, 42, 43, 45, 44, 47, 46, 48, 33, 34, 35, 37, 36, 39, 38, 40, 51, 52, 49, 50, 53, 67, 68, 69, 71, 70, 73, 72, 74, 77, 78, 75, 76, 79, 54
OFFSET
0,3
COMMENTS
We consider that a Fibonacci number is missing from the dual Zeckendorf representation of a number if it does not appear in this representation and a larger Fibonacci number appears in it.
The dual Zeckendorf representation is also known as the lazy Fibonacci representation (see A356771 for further details).
This sequence is a self-inverse permutation of the nonnegative integers.
EXAMPLE
The first terms, alongside the dual Zeckendorf representation in binary of n and of a(n), are:
n a(n) z(n) z(a(n))
-- ---- ----- -------
0 0 0 0
1 1 1 1
2 3 10 11
3 2 11 10
4 5 101 110
5 4 110 101
6 6 111 111
7 9 1010 1101
8 10 1011 1110
9 7 1101 1010
10 8 1110 1011
11 11 1111 1111
12 15 10101 11010
13 16 10110 11011
PROG
(PARI) \\ See Links section.
CROSSREFS
See A332022 for a similar sequence.
Sequence in context: A054069 A194869 A191736 * A297208 A372358 A301941
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 09 2024
STATUS
approved