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 (as there as infinitely many numbers whose dual Zeckendorf representations have no missing Fibonacci number); see A372656 for the inverse.
LINKS
EXAMPLE
The first terms, alongside their dual Zeckendorf representation in binary, are:
n a(n) z(a(n))
-- ---- -------
0 0 0
1 1 1
2 2 10
3 3 11
4 4 101
5 5 110
6 6 111
7 7 1010
8 9 1101
9 8 1011
10 10 1110
11 11 1111
12 12 10101
13 15 11010
14 14 10111
PROG
(PARI) \\ See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 09 2024
STATUS
approved