A370630 Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have exactly one common term.

1, 4, 3, 11, 8, 9, 6, 5, 7, 2, 10, 12, 14, 13, 15, 16, 18, 17, 20, 23, 21, 22, 19, 25, 26, 24, 27, 29, 28, 30, 35, 33, 37, 32, 38, 34, 36, 31, 41, 42, 39, 43, 47, 40, 44, 48, 45, 49, 46, 52, 60, 53, 56, 51, 58, 50, 59, 55, 57, 54, 61, 63, 62, 64, 68, 65, 69

Offset: 1

Author

Rémy Sigrist, May 01 2024

Keywords

• nonn
• base

Comments

Conjecture: this sequence is a permutation of the positive integers.

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

Crossrefs

Cf. A000120, A003714, A226077, A332565, A370631.

Programs

PARI

\\ See Links section.

Formula

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