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A372655
Lexicographically earliest sequence of distinct nonnegative integers such that the dual Zeckendorf representations of two consecutive terms have no common missing Fibonacci number.
3
0, 1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 11, 12, 15, 14, 16, 13, 17, 18, 19, 20, 25, 21, 26, 22, 27, 23, 29, 24, 28, 30, 31, 32, 33, 41, 35, 42, 34, 43, 36, 45, 37, 44, 38, 47, 40, 46, 39, 48, 49, 51, 50, 52, 53, 54, 67, 55, 68, 56, 69, 57, 71, 58, 70, 59, 73, 61, 72
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.
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
See A332565 for a similar sequence.
Cf. A356771, A361989, A372654, A372656 (inverse).
Sequence in context: A235489 A065306 A065307 * A356759 A372656 A375184
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 09 2024
STATUS
approved