A332022 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.

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, 35, 36, 37, 38, 39, 40, 41, 47, 25, 26, 27, 28, 29, 30, 31, 32, 55, 57, 56, 60, 62, 33, 58, 59, 61, 63, 64, 65, 66, 42, 44, 43, 48, 49, 45, 50, 46, 51, 52, 53, 54, 89

Offset: 0

Author

Rémy Sigrist, Apr 23 2020

Keywords

• nonn

Comments

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

Apparently, {a(0), ..., a(k)} = {0, ..., k} for infinitely many integers k.

Examples

			The first terms, alongside the Zeckendorf representation in binary of n and of a(n), are:
  n   a(n)  z(n)   z(a(n))
  --  ----  -----  -------
   0     0      0        0
   1     2      1       10
   2     1     10        1
   3     5    100     1000
   4     7    101     1010
   5     3   1000      100
   6     8   1001    10000
   7     4   1010      101
   8     6  10000     1001
   9    13  10001   100000
  10    14  10010   100001
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8360
• Rémy Sigrist, Scatterplot of (x, y) such that x and y have no common term in their Zeckendorf representations and 0 <= x, y <= 1218
• Rémy Sigrist, PARI program for A332022
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A003714, A238757 (binary analog), A332565.

Programs

PARI

See Links section.

Formula

A003714(n) AND A003714(a(n)) = 0 for any n >= 0 (where AND denotes the bitwise AND operator).