A376637 - OEIS

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

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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