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%I #16 Apr 25 2021 15:12:06
%S 0,1,2,3,4,5,7,6,8,11,10,9,12,13,18,16,15,20,14,19,17,21,29,26,24,32,
%T 23,31,30,22,28,27,25,33,34,47,42,39,52,37,50,49,36,48,45,44,54,35,43,
%U 41,40,53,38,51,46,55,76,68,63,84,60,81,79,58,78,77,73,87
%N Lexicographically latest sequence of distinct nonnegative terms such that for any n >= 0, n and a(n) have the same number of 0's and the same number of 1's in their Zeckendorf-binary representations.
%C This sequence is a self-inverse permutation of the nonnegative integers.
%H Rémy Sigrist, <a href="/A338698/b338698.txt">Table of n, a(n) for n = 0..10945</a>
%H Rémy Sigrist, <a href="/A338698/a338698.png">Colored scatterplot of the first F(21) terms</a> (where the color is function of A007895(n))
%H Rémy Sigrist, <a href="/A338698/a338698.gp.txt">PARI program for A338698</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A007895(a(n)) = A007895(n).
%F A072649(a(n)) = A072649(n) for any n > 0.
%F a(A000045(n)) = A000045(n).
%e The first terms, alongside their Zeckendorf-binary representation, are:
%e n a(n) zeck(n) zeck(a(n))
%e -- ---- ------- ----------
%e 0 0 0 0
%e 1 1 1 1
%e 2 2 10 10
%e 3 3 100 100
%e 4 4 101 101
%e 5 5 1000 1000
%e 6 7 1001 1010
%e 7 6 1010 1001
%e 8 8 10000 10000
%e 9 11 10001 10100
%e 10 10 10010 10010
%e 11 9 10100 10001
%e 12 12 10101 10101
%e 13 13 100000 100000
%e 14 18 100001 101000
%e 15 16 100010 100100
%e 16 15 100100 100010
%e 17 20 100101 101010
%e 18 14 101000 100001
%e 19 19 101001 101001
%e 20 17 101010 100101
%o (PARI) See Links section.
%Y Cf. A000045, A007895, A072649, A014417, A331274 (binary variant).
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Apr 24 2021
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