A352726 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have no common runs of consecutive 1's.

0, 2, 1, 4, 3, 6, 5, 8, 7, 12, 13, 14, 9, 10, 11, 16, 15, 24, 25, 26, 27, 28, 29, 30, 17, 18, 19, 20, 21, 22, 23, 32, 31, 48, 49, 50, 51, 54, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 33, 34, 35, 36, 38, 39, 37, 40, 41, 42, 43, 44, 45, 46, 47, 64, 63, 96, 97, 98

Offset

0,2

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

This sequence has similarities with A238757; here we consider runs of consecutive 1's, there individual 1's in binary expansions.

The binary expansion of n and a(n) may share some 1's, but cannot have a common run of consecutive 1's (as given by A352724).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, Scatterplot of the first 32769 terms

Rémy Sigrist, Scatterplot of (x, y) such that x, y < 2^10 and the binary expansions of x and y have no common runs of consecutive 1's

Rémy Sigrist, PARI program

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the corresponding partitions into runs of 1's, are:
  n   a(n)  runs in n  runs in a(n)
  --  ----  ---------  ------------
   0     0  []         []
   1     2  [1]        [2]
   2     1  [2]        [1]
   3     4  [3]        [4]
   4     3  [4]        [3]
   5     6  [1, 4]     [6]
   6     5  [6]        [1, 4]
   7     8  [7]        [8]
   8     7  [8]        [7]
   9    12  [1, 8]     [12]
  10    13  [2, 8]     [1, 12]
  11    14  [3, 8]     [14]
  12     9  [12]       [1, 8]
  13    10  [1, 12]    [2, 8]
  14    11  [14]       [3, 8]
  15    16  [15]       [16]
  16    15  [16]       [15]

Prog

(PARI) See Links section.

Crossrefs

Cf. A238757, A332022, A352724.

Sequence in context: A243500 A026262 A026234 * A317630 A282651 A282665

Adjacent sequences: A352723 A352724 A352725 * A352727 A352728 A352729

Keyword

nonn,base

Author

Rémy Sigrist, Mar 30 2022

Status

approved