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

Author

Rémy Sigrist, Aug 21 2018

Keywords

• nonn
• base
• look

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.

Examples

			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
		

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

Crossrefs

Cf. A066686, A303446.