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.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..10944
Rémy Sigrist, Scatterplot of the sequence for n = 0..28655
Rémy Sigrist, Scatterplot of (x, y) such that the dual Zeckendorf representations of x and y have no common missing term and x, y <= 1595
Rémy Sigrist, PARI program
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 09 2024
STATUS
approved