A352725 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of a(n) and a(n+1) have no common runs of consecutive 1's.

0, 1, 2, 3, 4, 6, 5, 7, 8, 12, 9, 14, 10, 13, 11, 15, 16, 24, 17, 26, 19, 25, 18, 27, 20, 28, 21, 30, 22, 29, 23, 31, 32, 48, 33, 50, 35, 49, 34, 51, 36, 54, 37, 55, 38, 52, 39, 53, 40, 56, 41, 58, 43, 57, 42, 59, 44, 60, 45, 62, 46, 61, 47, 63, 64, 96, 65, 98

Offset

0,3

Comments

This sequence is a variant of A109812; here we consider runs of consecutive 1's, there individual 1's in binary expansions.

The binary expansions of two consecutive terms 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, PARI program

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A109812, A332565, A352724.

Sequence in context: A330090 A072758 A104464 * A372128 A367307 A139706

Adjacent sequences: A352722 A352723 A352724 * A352726 A352727 A352728

Keyword

nonn,base

Author

Rémy Sigrist, Mar 30 2022

Status

approved