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A370630 Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have exactly one common term.

%I A370630 #16 May 04 2024 14:57:01
%S A370630 1,4,3,11,8,9,6,5,7,2,10,12,14,13,15,16,18,17,20,23,21,22,19,25,26,24,
%T A370630 27,29,28,30,35,33,37,32,38,34,36,31,41,42,39,43,47,40,44,48,45,49,46,
%U A370630 52,60,53,56,51,58,50,59,55,57,54,61,63,62,64,68,65,69
%N A370630 Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have exactly one common term.
%C A370630 Conjecture: this sequence is a permutation of the positive integers.
%H A370630 Rémy Sigrist, <a href="/A370630/b370630.txt">Table of n, a(n) for n = 1..10000</a>
%H A370630 Rémy Sigrist, <a href="/A370630/a370630.gp.txt">PARI program</a>
%H A370630 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A370630 A000120(A003714(a(n)), A003714(a(n+1))) = 1.
%e A370630 The first terms, alongside the Zeckendorf expansion in binary of a(n), are:
%e A370630   n   a(n)  z(a(n))
%e A370630   --  ----  -------
%e A370630    1     1        1
%e A370630    2     4      101
%e A370630    3     3      100
%e A370630    4    11    10100
%e A370630    5     8    10000
%e A370630    6     9    10001
%e A370630    7     6     1001
%e A370630    8     5     1000
%e A370630    9     7     1010
%e A370630   10     2       10
%e A370630   11    10    10010
%e A370630   12    12    10101
%o A370630 (PARI) \\ See Links section.
%Y A370630 Cf. A000120, A003714, A226077, A332565, A370631.
%K A370630 nonn,base
%O A370630 1,2
%A A370630 _Rémy Sigrist_, May 01 2024