A352728 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have exactly one common run of consecutive 1's.

1, 2, 3, 4, 9, 6, 7, 8, 5, 11, 10, 12, 17, 14, 15, 16, 13, 19, 18, 22, 23, 20, 21, 24, 26, 25, 35, 28, 33, 30, 31, 32, 29, 36, 27, 34, 38, 37, 40, 39, 44, 45, 46, 41, 42, 43, 79, 48, 50, 49, 52, 51, 54, 53, 71, 56, 58, 57, 67, 60, 65, 62, 63, 64, 61, 68, 59

Offset

1,2

Comments

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

This sequence is a variant of A238758; here we consider runs of consecutive 1's, there individual 1's in binary expansions.

We only consider runs of consecutive 1's that completely match in binary expansions of n and a(n), not simply single common 1's.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, Scatterplot of the first 24574 terms

Rémy Sigrist, Scatterplot of (x, y) such that x, y < 2^10 and the binary expansions of x and y exactly one common run 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 runs of 1's in binary expansions, are:
  n   a(n)  runs in n  runs in a(n)
  --  ----  ---------  ------------
   1     1  [1]        [1]
   2     2  [2]        [2]
   3     3  [3]        [3]
   4     4  [4]        [4]
   5     9  [1, 4]     [1, 8]
   6     6  [6]        [6]
   7     7  [7]        [7]
   8     8  [8]        [8]
   9     5  [1, 8]     [1, 4]
  10    11  [2, 8]     [3, 8]
  11    10  [3, 8]     [2, 8]
  12    12  [12]       [12]
  13    17  [1, 12]    [1, 16]
  14    14  [14]       [14]
  15    15  [15]       [15]
  16    16  [16]       [16]

Prog

(PARI) See Links section.

Crossrefs

Cf. A238758, A352726.

Sequence in context: A356886 A359416 A222248 * A236852 A363318 A236837

Adjacent sequences: A352725 A352726 A352727 * A352729 A352730 A352731

Keyword

nonn,base

Author

Rémy Sigrist, Mar 30 2022

Status

approved