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A318225 Lexicographically earliest sequence of positive terms such that the concatenation of two consecutive terms is always unique. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A335497 A309872 A248034

Adjacent sequences:  A318222 A318223 A318224 * A318226 A318227 A318228

KEYWORD

nonn,base,look

AUTHOR

Rémy Sigrist, Aug 21 2018

STATUS

approved

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Last modified July 24 05:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)