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 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.
LINKS
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 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
PROG
(PARI) \\ See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 09 2024
STATUS
approved