A372659 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the Fibonacci numbers that appear in the Zeckendorf representation of n do not appear in the dual Zeckendorf representation of a(n).

0, 2, 1, 3, 20, 4, 15, 12, 5, 7, 13, 8, 29, 6, 10, 21, 16, 36, 9, 19, 63, 11, 18, 17, 28, 33, 14, 26, 59, 22, 54, 56, 57, 101, 23, 34, 25, 27, 96, 46, 53, 88, 24, 44, 51, 42, 211, 38, 49, 93, 92, 180, 47, 91, 207, 30, 37, 64, 50, 62, 43, 60, 80, 31, 41, 85, 76

Offset: 0

Author

Rémy Sigrist, May 09 2024

Keywords

• nonn
• base

Comments

The dual Zeckendorf representation is also known as the lazy Fibonacci representation (see A356771 for further details).

This sequence is a permutation of the nonnegative integers with inverse A372660.

Examples

			The first terms, alongside the Zeckendorf representation of n and the dual Zeckendorf representation of a(n), in binary, are:
  n   a(n)  z(n)    d(a(n))
  --  ----  ------  --------
   0     0       0         0
   1     2       1        10
   2     1      10         1
   3     3     100        10
   4    20     101    101010
   5     4    1000       101
   6    15    1001    110110
   7    12    1010     10101
   8     5   10000       111
   9     7   10001      1110
  10    13   10010    101101
  11     8   10100      1011
  12    29   10101  10101010
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..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

Crossrefs

See A372657 for a similar sequence.

Cf. A356771, A372660 (inverse).

Programs

PARI

\\ See Links section.