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

Author

Rémy Sigrist, May 01 2024

Keywords

• nonn
• base

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.

Examples

			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
		

Links

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

Programs

PARI

\\ See Links section.

Formula

A000120(A003714(a(n)), A003714(a(n+1))) > 0.