A318225 Lexicographically earliest sequence of positive terms such that the concatenation of two consecutive terms is always unique.

1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 2, 11, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 10, 3, 11, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 4, 10, 4, 11, 5, 5, 6, 5, 7, 5, 8, 5, 9, 5, 10, 5

Offset

1,3

Comments

In other words, for any distinct i and j, A066686(a(i), a(i+1)) <> A066686(a(j), a(j+1)).

The sequence b such that for any n > 0, b(n) = A066686(a(n), a(n+1)), satisfies b(n) = A303446(n+1) for n = 1..116 and b(117) <> A303446(118).

The sequence contains long runs of consecutive terms where one term out of two equals 1.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Logarithmic density plot of the first 300000000 terms

Rémy Sigrist, C++ program for A318225

Example

The first terms, alongside the concatenation of a(n) and of a(n+1), are:
  n  a(n)   A066686(a(n), a(n+1))
  -- ----   ---------------------
   1    1    11
   2    1    12
   3    2    21
   4    1    13
   5    3    31
   6    1    14
   7    4    41
   8    1    15
   9    5    51
  10    1    16
  11    6    61
  12    1    17
  13    7    71
  14    1    18
  15    8    81
  16    1    19
  17    9    91
  18    1   110
  19   10   101
  20    1   111
  21   11   112
  22    2    22
  23    2    23
  24    3    32
  25    2    24

Prog

(C++) See Links section.

Crossrefs

Cf. A066686, A303446.

Sequence in context: A152271 A133622 A158416 * A360257 A335497 A309872

Adjacent sequences: A318222 A318223 A318224 * A318226 A318227 A318228

Keyword

nonn,base,look

Author

Rémy Sigrist, Aug 21 2018

Status

approved