A370629 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the Zeckendorf expansions of n and a(n) have exactly one common term.

1, 2, 3, 6, 5, 4, 10, 8, 11, 7, 9, 14, 13, 12, 16, 15, 18, 17, 22, 23, 21, 19, 20, 26, 28, 24, 29, 25, 27, 35, 36, 37, 40, 34, 30, 31, 32, 39, 38, 33, 42, 41, 47, 48, 49, 52, 43, 44, 45, 58, 56, 46, 59, 57, 55, 51, 54, 50, 53, 63, 65, 64, 60, 62, 61, 68, 70

Offset: 1

Author

Rémy Sigrist, May 01 2024

Keywords

• nonn
• base

Comments

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

Fixed points correspond to positive Fibonacci numbers.

Examples

			The first terms, alongside the Zeckendorf expansion in binary of n and of a(n), are:
  n   a(n)  z(n)    z(a(n))
  --  ----  ------  -------
   1     1       1        1
   2     2      10       10
   3     3     100      100
   4     6     101     1001
   5     5    1000     1000
   6     4    1001      101
   7    10    1010    10010
   8     8   10000    10000
   9    11   10001    10100
  10     7   10010     1010
  11     9   10100    10001
  12    14   10101   100001
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program
• Index entries for sequences related to Zeckendorf expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000120, A003714, A238758, A332022.

Programs

PARI

\\ See Links section.

Formula

A000120(A003714(n), A003714(a(n))) = 1.