A332565 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and a(n+1) have no common term in their Zeckendorf representations.

0, 1, 2, 3, 5, 4, 7, 8, 6, 10, 13, 9, 15, 11, 14, 21, 12, 18, 22, 16, 23, 17, 26, 34, 19, 24, 20, 25, 36, 27, 37, 28, 35, 29, 38, 31, 39, 30, 41, 32, 40, 55, 33, 47, 56, 42, 57, 43, 58, 44, 59, 49, 60, 45, 61, 50, 62, 46, 68, 89, 48, 63, 51, 65, 52, 64, 54, 66

Offset: 0

Author

Rémy Sigrist, Apr 23 2020

Keywords

• nonn

Comments

This sequence is a permutation of the natural numbers.

Examples

			The first terms, alongside their Zeckendorf representation in binary, are:
  n   a(n)  bin(A003714(a(n)))
  --  ----  ------------------
   0     0                   0
   1     1                   1
   2     2                  10
   3     3                 100
   4     5                1000
   5     4                 101
   6     7                1010
   7     8               10000
   8     6                1001
   9    10               10010
  10    13              100000
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program for A332565
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A003714, A109812 (binary analog), A332022.

Programs

PARI

See Links section.

Formula

A003714(a(n)) AND A003714(a(n+1)) = 0 for any n >= 0 (where AND denotes the bitwise AND operator).