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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.

%I A372655 #13 May 12 2024 11:24:32
%S A372655 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,
%T A372655 23,29,24,28,30,31,32,33,41,35,42,34,43,36,45,37,44,38,47,40,46,39,48,
%U A372655 49,51,50,52,53,54,67,55,68,56,69,57,71,58,70,59,73,61,72
%N A372655 Lexicographically earliest sequence of distinct nonnegative integers such that the dual Zeckendorf representations of two consecutive terms have no common missing Fibonacci number.
%C A372655 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.
%C A372655 The dual Zeckendorf representation is also known as the lazy Fibonacci representation (see A356771 for further details).
%C A372655 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.
%H A372655 Rémy Sigrist, <a href="/A372655/b372655.txt">Table of n, a(n) for n = 0..10000</a>
%H A372655 Rémy Sigrist, <a href="/A372655/a372655.gp.txt">PARI program</a>
%H A372655 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%H A372655 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A372655 The first terms, alongside their dual Zeckendorf representation in binary, are:
%e A372655   n   a(n)  z(a(n))
%e A372655   --  ----  -------
%e A372655    0     0        0
%e A372655    1     1        1
%e A372655    2     2       10
%e A372655    3     3       11
%e A372655    4     4      101
%e A372655    5     5      110
%e A372655    6     6      111
%e A372655    7     7     1010
%e A372655    8     9     1101
%e A372655    9     8     1011
%e A372655   10    10     1110
%e A372655   11    11     1111
%e A372655   12    12    10101
%e A372655   13    15    11010
%e A372655   14    14    10111
%o A372655 (PARI) \\ See Links section.
%Y A372655 See A332565 for a similar sequence.
%Y A372655 Cf. A356771, A361989, A372654, A372656 (inverse).
%K A372655 nonn,base
%O A372655 0,3
%A A372655 _Rémy Sigrist_, May 09 2024