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A370629 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the Zeckendorf expansions of n and a(n) have exactly one common term.

%I A370629 #16 May 04 2024 14:56:51
%S A370629 1,2,3,6,5,4,10,8,11,7,9,14,13,12,16,15,18,17,22,23,21,19,20,26,28,24,
%T A370629 29,25,27,35,36,37,40,34,30,31,32,39,38,33,42,41,47,48,49,52,43,44,45,
%U A370629 58,56,46,59,57,55,51,54,50,53,63,65,64,60,62,61,68,70
%N A370629 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the Zeckendorf expansions of n and a(n) have exactly one common term.
%C A370629 This sequence is a self-inverse permutation of the positive integers.
%C A370629 Fixed points correspond to positive Fibonacci numbers.
%H A370629 Rémy Sigrist, <a href="/A370629/b370629.txt">Table of n, a(n) for n = 1..10000</a>
%H A370629 Rémy Sigrist, <a href="/A370629/a370629.gp.txt">PARI program</a>
%H A370629 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%H A370629 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A370629 A000120(A003714(n), A003714(a(n))) = 1.
%e A370629 The first terms, alongside the Zeckendorf expansion in binary of n and of a(n), are:
%e A370629   n   a(n)  z(n)    z(a(n))
%e A370629   --  ----  ------  -------
%e A370629    1     1       1        1
%e A370629    2     2      10       10
%e A370629    3     3     100      100
%e A370629    4     6     101     1001
%e A370629    5     5    1000     1000
%e A370629    6     4    1001      101
%e A370629    7    10    1010    10010
%e A370629    8     8   10000    10000
%e A370629    9    11   10001    10100
%e A370629   10     7   10010     1010
%e A370629   11     9   10100    10001
%e A370629   12    14   10101   100001
%o A370629 (PARI) \\ See Links section.
%Y A370629 Cf. A000120, A003714, A238758, A332022.
%K A370629 nonn,base
%O A370629 1,2
%A A370629 _Rémy Sigrist_, May 01 2024