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%I #34 Apr 27 2020 08:16:26
%S 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 20,25,36,27,37,28,35,29,38,31,39,30,41,32,40,55,33,47,56,42,57,43,58,
%U 44,59,49,60,45,61,50,62,46,68,89,48,63,51,65,52,64,54,66
%N 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 This sequence is a permutation of the natural numbers.
%H Rémy Sigrist, <a href="/A332565/b332565.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A332565/a332565.gp.txt">PARI program for A332565</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A003714(a(n)) AND A003714(a(n+1)) = 0 for any n >= 0 (where AND denotes the bitwise AND operator).
%e The first terms, alongside their Zeckendorf representation in binary, are:
%e n a(n) bin(A003714(a(n)))
%e -- ---- ------------------
%e 0 0 0
%e 1 1 1
%e 2 2 10
%e 3 3 100
%e 4 5 1000
%e 5 4 101
%e 6 7 1010
%e 7 8 10000
%e 8 6 1001
%e 9 10 10010
%e 10 13 100000
%o (PARI) See Links section.
%Y Cf. A003714, A109812 (binary analog), A332022.
%K nonn
%O 0,3
%A _Rémy Sigrist_, Apr 23 2020
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