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.

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, 23, 31, 30, 22, 28, 27, 25, 33, 34, 47, 42, 39, 52, 37, 50, 49, 36, 48, 45, 44, 54, 35, 43, 41, 40, 53, 38, 51, 46, 55, 76, 68, 63, 84, 60, 81, 79, 58, 78, 77, 73, 87

Offset

0,3

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10945

Rémy Sigrist, Colored scatterplot of the first F(21) terms (where the color is function of A007895(n))

Rémy Sigrist, PARI program for A338698

Index entries for sequences that are permutations of the natural numbers

Formula

A007895(a(n)) = A007895(n).

A072649(a(n)) = A072649(n) for any n > 0.

a(A000045(n)) = A000045(n).

Example

The first terms, alongside their Zeckendorf-binary representation, are:
  n   a(n)  zeck(n)  zeck(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     2       10          10
   3     3      100         100
   4     4      101         101
   5     5     1000        1000
   6     7     1001        1010
   7     6     1010        1001
   8     8    10000       10000
   9    11    10001       10100
  10    10    10010       10010
  11     9    10100       10001
  12    12    10101       10101
  13    13   100000      100000
  14    18   100001      101000
  15    16   100010      100100
  16    15   100100      100010
  17    20   100101      101010
  18    14   101000      100001
  19    19   101001      101001
  20    17   101010      100101

Prog

(PARI) See Links section.

Crossrefs

Cf. A000045, A007895, A072649, A014417, A331274 (binary variant).

Sequence in context: A056017 A091995 A343150 * A361946 A066937 A217266

Adjacent sequences: A338695 A338696 A338697 * A338699 A338700 A338701

Keyword

nonn,base

Author

Rémy Sigrist, Apr 24 2021

Status

approved