A370631 Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have at least one common term.

1, 4, 3, 11, 8, 9, 6, 5, 7, 2, 10, 12, 14, 13, 15, 16, 17, 18, 19, 20, 23, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67

Offset

1,2

Comments

This sequence is a permutation of the positive integers with inverse A370632:

- for k >= 7, the values whose Zeckendorf expansions have largest term A000045(k) appear in a single run of consecutive values; the first value being A000045(k) + 1 or 2, the second value being A000045(k), the remaining values appearing in ascending order.

Links

Table of n, a(n) for n=1..67.

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(a(n)), A003714(a(n+1))) > 0.

Example

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

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A000045, A000120, A003714, A115510, A370630, A370632 (inverse).

Sequence in context: A072183 A353341 A346614 * A370630 A005013 A241643

Adjacent sequences: A370628 A370629 A370630 * A370632 A370633 A370634

Keyword

nonn,base

Author

Rémy Sigrist, May 01 2024

Status

approved