A352836 Lexicographically earliest sequence of positive integers such that the binary expansions of two consecutive terms have a 1 at the same position and for any distinct m and n, {a(m), a(m+1)} <> {a(n), a(n+1)}.

1, 1, 3, 2, 2, 6, 3, 3, 5, 1, 7, 2, 10, 3, 7, 4, 4, 5, 5, 6, 4, 12, 5, 7, 6, 6, 10, 7, 7, 9, 1, 11, 2, 14, 3, 9, 5, 11, 3, 13, 1, 15, 2, 18, 3, 15, 4, 13, 5, 14, 4, 20, 5, 15, 6, 11, 7, 12, 6, 13, 7, 14, 6, 18, 7, 15, 8, 8, 9, 9, 10, 8, 11, 9, 12, 8, 13, 9, 14

Offset

1,3

Links

Rémy Sigrist, Table of n, a(n) for n = 1..9999

Rémy Sigrist, Colored scatterplot of (a(n), a(n+1)) for n < 2^18 (where the hue is function of n)

Rémy Sigrist, C++ program

Example

The first terms, alongside their binary expansion and {a(n), a(n+1)}, are:
  n   a(n)  bin(a(n))  {a(n), a(n+1)}
  --  ----  ---------  --------------
   1     1          1  {1}
   2     1          1  {1, 3}
   3     3         11  {2, 3}
   4     2         10  {2}
   5     2         10  {2, 6}
   6     6        110  {3, 6}
   7     3         11  {3}
   8     3         11  {3, 5}
   9     5        101  {1, 5}
  10     1          1  {1, 7}
  11     7        111  {2, 7}
  12     2         10  {2, 10}
  13    10       1010  {3, 10}
  14     3         11  {3, 7}
  15     7        111  {4, 7}

Prog

(C++) See Links section.

Crossrefs

Cf. A352835.

Sequence in context: A285733 A106335 A218698 * A065474 A272332 A197586

Adjacent sequences: A352833 A352834 A352835 * A352837 A352838 A352839

Keyword

nonn,look,base

Author

Rémy Sigrist, Apr 05 2022

Status

approved