A372655 - OEIS

%I #13 May 12 2024 11:24:32

%S 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 23,29,24,28,30,31,32,33,41,35,42,34,43,36,45,37,44,38,47,40,46,39,48,

%U 49,51,50,52,53,54,67,55,68,56,69,57,71,58,70,59,73,61,72

%N Lexicographically earliest sequence of distinct nonnegative integers such that the dual Zeckendorf representations of two consecutive terms have no common missing Fibonacci number.

%C 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 The dual Zeckendorf representation is also known as the lazy Fibonacci representation (see A356771 for further details).

%C 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 Rémy Sigrist, <a href="/A372655/b372655.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A372655/a372655.gp.txt">PARI program</a>

%H <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The first terms, alongside their dual Zeckendorf representation in binary, are:

%e   n   a(n)  z(a(n))

%e   --  ----  -------

%e    0     0        0

%e    1     1        1

%e    2     2       10

%e    3     3       11

%e    4     4      101

%e    5     5      110

%e    6     6      111

%e    7     7     1010

%e    8     9     1101

%e    9     8     1011

%e   10    10     1110

%e   11    11     1111

%e   12    12    10101

%e   13    15    11010

%e   14    14    10111

%o (PARI) \\ See Links section.

%Y See A332565 for a similar sequence.

%Y Cf. A356771, A361989, A372654, A372656 (inverse).

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, May 09 2024