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

1,2

Comments

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

Fixed points correspond to positive Fibonacci numbers.

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

Formula

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

Example

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

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A000120, A003714, A238758, A332022.

Sequence in context: A254118 A056895 A254117 * A218890 A269373 A269374

Adjacent sequences: A370625 A370626 A370628 * A370630 A370631 A370632

Keyword

nonn,base

Author

Rémy Sigrist, May 01 2024

Status

approved