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

0,3

Comments

This sequence is a permutation of the natural numbers.

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

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A257455 A328971 A127515 * A256996 A316668 A099424

Adjacent sequences: A332562 A332563 A332564 * A332566 A332567 A332568

Keyword

nonn

Author

Rémy Sigrist, Apr 23 2020

Status

approved