A372654 - OEIS

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

%S 0,1,3,2,5,4,6,9,10,7,8,11,15,16,17,12,13,14,19,18,25,26,27,29,28,20,

%T 21,22,24,23,31,30,32,41,42,43,45,44,47,46,48,33,34,35,37,36,39,38,40,

%U 51,52,49,50,53,67,68,69,71,70,73,72,74,77,78,75,76,79,54

%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the dual Zeckendorf representations of n and a(n) 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 self-inverse permutation of the nonnegative integers.

%H Rémy Sigrist, <a href="/A372654/b372654.txt">Table of n, a(n) for n = 0..10944</a>

%H Rémy Sigrist, <a href="/A372654/a372654_1.png">Scatterplot of the sequence for n = 0..28655</a>

%H Rémy Sigrist, <a href="/A372654/a372654.png">Scatterplot of (x, y) such that the dual Zeckendorf representations of x and y have no common missing term and x, y <= 1595</a>

%H Rémy Sigrist, <a href="/A372654/a372654.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 the dual Zeckendorf representation in binary of n and of a(n), are:

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

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

%e    0     0      0        0

%e    1     1      1        1

%e    2     3     10       11

%e    3     2     11       10

%e    4     5    101      110

%e    5     4    110      101

%e    6     6    111      111

%e    7     9   1010     1101

%e    8    10   1011     1110

%e    9     7   1101     1010

%e   10     8   1110     1011

%e   11    11   1111     1111

%e   12    15  10101    11010

%e   13    16  10110    11011

%o (PARI) \\ See Links section.

%Y See A332022 for a similar sequence.

%Y Cf. A356771, A361989, A372655.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, May 09 2024