A372659 - OEIS

%I #9 May 12 2024 11:25:05

%S 0,2,1,3,20,4,15,12,5,7,13,8,29,6,10,21,16,36,9,19,63,11,18,17,28,33,

%T 14,26,59,22,54,56,57,101,23,34,25,27,96,46,53,88,24,44,51,42,211,38,

%U 49,93,92,180,47,91,207,30,37,64,50,62,43,60,80,31,41,85,76

%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the Fibonacci numbers that appear in the Zeckendorf representation of n do not appear in the dual Zeckendorf representation of a(n).

%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 with inverse A372660.

%H Rémy Sigrist, <a href="/A372659/b372659.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A372659/a372659.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 Zeckendorf representation of n and the dual Zeckendorf representation of a(n), in binary, are:

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

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

%e    0     0       0         0

%e    1     2       1        10

%e    2     1      10         1

%e    3     3     100        10

%e    4    20     101    101010

%e    5     4    1000       101

%e    6    15    1001    110110

%e    7    12    1010     10101

%e    8     5   10000       111

%e    9     7   10001      1110

%e   10    13   10010    101101

%e   11     8   10100      1011

%e   12    29   10101  10101010

%o (PARI) \\ See Links section.

%Y See A372657 for a similar sequence.

%Y Cf. A356771, A372660 (inverse).

%K nonn,base

%O 0,2

%A _Rémy Sigrist_, May 09 2024