A376637 The word 1 belongs to the sequence, and whenever a word w belongs to the sequence, then the words consisting of 1's and 2's whose run lengths transform equals w also belong to the sequence.

1, 2, 11, 12, 21, 22, 112, 122, 211, 221, 1121, 1122, 1211, 2122, 2211, 2212, 11221, 12112, 12211, 12212, 21121, 21122, 21221, 22112, 112212, 121122, 212211, 221121, 1121122, 1121221, 1122122, 1211221, 1221121, 1221211, 2112122, 2112212, 2122112, 2211211

Offset

1,2

Comments

This sequence lists finite smooth words: finite words w composed of 1's and 2's without three or more consecutive equal digits, such that for any k > 0, the k-th iterate of the run lengths transform of w is also a word composed of 1's and 2's without three or more consecutive equal digits.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10048

Geneviève Paquin, Srĕcko Brlek, Damien Jamet, Extremal generalized smooth words

Rémy Sigrist, Illustration of the first terms (arrows denotes run lengths transforms)

Rémy Sigrist, PARI program

Index entries for sequences related to Kolakoski sequence

Example

The first terms, alongside their run lengths transform, are:
  n   a(n)  RL(a(n))
  --  ----  --------
   1     1         1
   2     2         1
   3    11         2
   4    12        11
   5    21        11
   6    22         2
   7   112        21
   8   122        12
   9   211        12
  10   221        21
  11  1121       211
  12  1122        22
  13  1211       112
  14  2122       112
  15  2211        22
  16  2212       211

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A000002, A007931, A376638, A376674, A376676, A376685, A376698.

Sequence in context: A136407 A376677 A214215 * A136999 A271372 A053880

Adjacent sequences: A376634 A376635 A376636 * A376638 A376639 A376640

Keyword

nonn,base

Author

Rémy Sigrist, Sep 30 2024

Status

approved