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%I #24 Apr 27 2020 08:16:30
%S 0,2,1,5,7,3,8,4,6,13,14,15,18,9,10,11,21,23,12,24,22,16,20,17,19,34,
%T 35,36,37,38,39,40,41,47,25,26,27,28,29,30,31,32,55,57,56,60,62,33,58,
%U 59,61,63,64,65,66,42,44,43,48,49,45,50,46,51,52,53,54,89
%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) have no common term in their Zeckendorf representations.
%C This sequence is a self-inverse permutation of the nonnegative integers.
%C Apparently, {a(0), ..., a(k)} = {0, ..., k} for infinitely many integers k.
%H Rémy Sigrist, <a href="/A332022/b332022.txt">Table of n, a(n) for n = 0..8360</a>
%H Rémy Sigrist, <a href="/A332022/a332022.png">Scatterplot of (x, y) such that x and y have no common term in their Zeckendorf representations and 0 <= x, y <= 1218</a>
%H Rémy Sigrist, <a href="/A332022/a332022.gp.txt">PARI program for A332022</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A003714(n) AND A003714(a(n)) = 0 for any n >= 0 (where AND denotes the bitwise AND operator).
%e The first terms, alongside the Zeckendorf representation in binary of n and of a(n), are:
%e n a(n) z(n) z(a(n))
%e -- ---- ----- -------
%e 0 0 0 0
%e 1 2 1 10
%e 2 1 10 1
%e 3 5 100 1000
%e 4 7 101 1010
%e 5 3 1000 100
%e 6 8 1001 10000
%e 7 4 1010 101
%e 8 6 10000 1001
%e 9 13 10001 100000
%e 10 14 10010 100001
%o (PARI) See Links section.
%Y Cf. A003714, A238757 (binary analog), A332565.
%K nonn
%O 0,2
%A _Rémy Sigrist_, Apr 23 2020
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