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A372657
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Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the Fibonacci numbers that appear in the Zeckendorf representation of n are not missing from the dual Zeckendorf representation of a(n).
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3
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 16, 21, 18, 20, 22, 23, 24, 25, 28, 29, 31, 26, 27, 32, 30, 33, 34, 35, 36, 38, 40, 37, 42, 39, 46, 48, 47, 51, 53, 41, 43, 44, 45, 56, 49, 50, 52, 54, 55, 57, 58, 59, 62, 63, 65, 60, 61, 66, 64, 67
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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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 permutation of the nonnegative integers with inverse A372658: for any v >= 0, the majority of Fibonacci numbers are not missing from the dual Zeckendorf representation of v, and provide opportunities for v to be chosen, and so v will eventually appear in the sequence.
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LINKS
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EXAMPLE
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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 1 1 1
2 2 10 10
3 3 100 11
4 4 101 101
5 5 1000 110
6 6 1001 111
7 7 1010 1010
8 8 10000 1011
9 9 10001 1101
10 10 10010 1110
11 11 10100 1111
12 12 10101 10101
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PROG
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(PARI) \\ See Links section.
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CROSSREFS
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See A372659 for a similar sequence.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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