cp's OEIS Frontend

A338698 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.

%I A338698 #16 Apr 25 2021 15:12:06
%S A338698 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 A338698 23,31,30,22,28,27,25,33,34,47,42,39,52,37,50,49,36,48,45,44,54,35,43,
%U A338698 41,40,53,38,51,46,55,76,68,63,84,60,81,79,58,78,77,73,87
%N A338698 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 A338698 This sequence is a self-inverse permutation of the nonnegative integers.
%H A338698 Rémy Sigrist, <a href="/A338698/b338698.txt">Table of n, a(n) for n = 0..10945</a>
%H A338698 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 A338698 Rémy Sigrist, <a href="/A338698/a338698.gp.txt">PARI program for A338698</a>
%H A338698 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A338698 A007895(a(n)) = A007895(n).
%F A338698 A072649(a(n)) = A072649(n) for any n > 0.
%F A338698 a(A000045(n)) = A000045(n).
%e A338698 The first terms, alongside their Zeckendorf-binary representation, are:
%e A338698   n   a(n)  zeck(n)  zeck(a(n))
%e A338698   --  ----  -------  ----------
%e A338698    0     0        0           0
%e A338698    1     1        1           1
%e A338698    2     2       10          10
%e A338698    3     3      100         100
%e A338698    4     4      101         101
%e A338698    5     5     1000        1000
%e A338698    6     7     1001        1010
%e A338698    7     6     1010        1001
%e A338698    8     8    10000       10000
%e A338698    9    11    10001       10100
%e A338698   10    10    10010       10010
%e A338698   11     9    10100       10001
%e A338698   12    12    10101       10101
%e A338698   13    13   100000      100000
%e A338698   14    18   100001      101000
%e A338698   15    16   100010      100100
%e A338698   16    15   100100      100010
%e A338698   17    20   100101      101010
%e A338698   18    14   101000      100001
%e A338698   19    19   101001      101001
%e A338698   20    17   101010      100101
%o A338698 (PARI) See Links section.
%Y A338698 Cf. A000045, A007895, A072649, A014417, A331274 (binary variant).
%K A338698 nonn,base
%O A338698 0,3
%A A338698 _Rémy Sigrist_, Apr 24 2021