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A332565 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and a(n+1) have no common term in their Zeckendorf representations.

%I A332565 #34 Apr 27 2020 08:16:26
%S A332565 0,1,2,3,5,4,7,8,6,10,13,9,15,11,14,21,12,18,22,16,23,17,26,34,19,24,
%T A332565 20,25,36,27,37,28,35,29,38,31,39,30,41,32,40,55,33,47,56,42,57,43,58,
%U A332565 44,59,49,60,45,61,50,62,46,68,89,48,63,51,65,52,64,54,66
%N A332565 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and a(n+1) have no common term in their Zeckendorf representations.
%C A332565 This sequence is a permutation of the natural numbers.
%H A332565 Rémy Sigrist, <a href="/A332565/b332565.txt">Table of n, a(n) for n = 0..10000</a>
%H A332565 Rémy Sigrist, <a href="/A332565/a332565.gp.txt">PARI program for A332565</a>
%H A332565 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A332565 A003714(a(n)) AND A003714(a(n+1)) = 0 for any n >= 0 (where AND denotes the bitwise AND operator).
%e A332565 The first terms, alongside their Zeckendorf representation in binary, are:
%e A332565   n   a(n)  bin(A003714(a(n)))
%e A332565   --  ----  ------------------
%e A332565    0     0                   0
%e A332565    1     1                   1
%e A332565    2     2                  10
%e A332565    3     3                 100
%e A332565    4     5                1000
%e A332565    5     4                 101
%e A332565    6     7                1010
%e A332565    7     8               10000
%e A332565    8     6                1001
%e A332565    9    10               10010
%e A332565   10    13              100000
%o A332565 (PARI) See Links section.
%Y A332565 Cf. A003714, A109812 (binary analog), A332022.
%K A332565 nonn
%O A332565 0,3
%A A332565 _Rémy Sigrist_, Apr 23 2020