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

0,2

Comments

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

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

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

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A369527 A370382 A059039 * A109261 A085240 A002251

Adjacent sequences: A332019 A332020 A332021 * A332023 A332024 A332025

Keyword

nonn

Author

Rémy Sigrist, Apr 23 2020

Status

approved