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

Author

Rémy Sigrist, Apr 24 2021

Keywords

• nonn
• base

Comments

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

Examples

			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
		

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

Crossrefs

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

Programs

PARI

See Links section.

Formula

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

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

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