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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.

%I A376637 #19 Oct 03 2024 11:02:26
%S A376637 1,2,11,12,21,22,112,122,211,221,1121,1122,1211,2122,2211,2212,11221,
%T A376637 12112,12211,12212,21121,21122,21221,22112,112212,121122,212211,
%U A376637 221121,1121122,1121221,1122122,1211221,1221121,1221211,2112122,2112212,2122112,2211211
%N 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.
%C A376637 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.
%H A376637 Geneviève Paquin, Srĕcko Brlek, Damien Jamet, <a href="https://www.irisa.fr/JM06/Slides/SlidesPaquinBrlek.pdf">Extremal generalized smooth words</a>
%H A376637 Rémy Sigrist, <a href="/A376637/b376637.txt">Table of n, a(n) for n = 1..10048</a>
%H A376637 Rémy Sigrist, <a href="/A376637/a376637.png">Illustration of the first terms</a> (arrows denotes run lengths transforms)
%H A376637 Rémy Sigrist, <a href="/A376637/a376637.gp.txt">PARI program</a>
%H A376637 <a href="/index/K#Kolakoski">Index entries for sequences related to Kolakoski sequence</a>
%e A376637 The first terms, alongside their run lengths transform, are:
%e A376637   n   a(n)  RL(a(n))
%e A376637   --  ----  --------
%e A376637    1     1         1
%e A376637    2     2         1
%e A376637    3    11         2
%e A376637    4    12        11
%e A376637    5    21        11
%e A376637    6    22         2
%e A376637    7   112        21
%e A376637    8   122        12
%e A376637    9   211        12
%e A376637   10   221        21
%e A376637   11  1121       211
%e A376637   12  1122        22
%e A376637   13  1211       112
%e A376637   14  2122       112
%e A376637   15  2211        22
%e A376637   16  2212       211
%o A376637 (PARI) \\ See Links section.
%Y A376637 Cf. A000002, A007931, A376638, A376674, A376676, A376685, A376698.
%K A376637 nonn,base
%O A376637 1,2
%A A376637 _Rémy Sigrist_, Sep 30 2024