A340447 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) XOR a(n+1) is a Fibonacci number as small as possible (where XOR denotes the bitwise XOR operator).

0, 1, 3, 2, 7, 6, 4, 5, 13, 12, 14, 15, 10, 11, 9, 8, 29, 28, 30, 31, 26, 27, 25, 24, 16, 17, 19, 18, 23, 22, 20, 21, 55, 54, 52, 53, 48, 49, 51, 50, 58, 59, 57, 56, 61, 60, 62, 63, 42, 43, 41, 40, 45, 44, 46, 47, 39, 38, 36, 37, 32, 33, 35, 34, 123, 122, 120

Offset

0,3

Comments

This sequence appears to be a permutation of the nonnegative integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, Scatterplot of the first 2^16 terms

Example

The first terms, alongside a(n) XOR a(n+1), are:
  n   a(n)  a(n) XOR a(n+1)
  --  ----  ---------------
   0     0                1
   1     1                2
   2     3                1
   3     2                5
   4     7                1
   5     6                2
   6     4                1
   7     5                8
   8    13                1
   9    12                2
  10    14                1
  11    15                5
  12    10                1
  13    11                2
  14     9                1
  15     8               21

Prog

(PARI) s=0; v=0; for (n=0, 66, print1 (v", "); s+=2^v; for (k=1, oo, if (!bittest(s, w=bitxor(v, fibonacci(k))), v=w; break)))

Crossrefs

See A340406 for similar sequences.

Cf. A000045.

Sequence in context: A283997 A096899 A265345 * A360983 A154448 A099896

Adjacent sequences: A340444 A340445 A340446 * A340448 A340449 A340450

Keyword

nonn

Author

Rémy Sigrist, Jan 07 2021

Status

approved