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A347290 Arnoux-Rauzy word sigma_0 x sigma_2 x sigma_1. Fixed point of the morphism 0-> 0201020, 1->1020, 2->201020 starting from a(1)=0.

%I A347290 #35 Jun 20 2025 16:37:33
%S A347290 0,2,0,1,0,2,0,2,0,1,0,2,0,0,2,0,1,0,2,0,1,0,2,0,0,2,0,1,0,2,0,2,0,1,
%T A347290 0,2,0,0,2,0,1,0,2,0,2,0,1,0,2,0,0,2,0,1,0,2,0,1,0,2,0,0,2,0,1,0,2,0,
%U A347290 2,0,1,0,2,0,0
%N A347290 Arnoux-Rauzy word sigma_0 x sigma_2 x sigma_1. Fixed point of the morphism 0-> 0201020, 1->1020, 2->201020 starting from a(1)=0.
%C A347290 Arnoux-Rauzy word sigma_0 x sigma_2 x sigma_1, where sigmas are defined as:
%C A347290   sigma_0 : 0 -> 0, 1 -> 10, 2 -> 20;
%C A347290   sigma_1 : 0 -> 01, 1 -> 1, 2 -> 21;
%C A347290   sigma_2 : 0 -> 02, 1 -> 12, 2 -> 2.
%C A347290 Fixed point of the morphism 0->0201020, 1->1020, 2->201020 starting from a(1)=0.
%C A347290 Frequency of letters:
%C A347290   0: 1/t   ~ 54.368% (A192918)
%C A347290   1: 1/t^3 ~ 16.071%
%C A347290   2: 1/t^2 ~ 29.559%
%C A347290 where t is tribonacci constant A058265.
%C A347290 Equals A286998 with a re-mapping of values 1->2, 2->1.
%H A347290 L. Balková, M. Bucci, A. De Luca, J. Hladký and S. Puzynina, <a href="https://doi.org/10.1016/j.tcs.2016.07.042">Aperiodic Pseudorandom Number Generators Based on Infinite Words</a>, Theoret. Comput. Sci. 647 (2016), 85-100.
%H A347290 Julien Cassaigne, Sebastien Ferenczi, and Luca Q. Zamboni, <a href="http://www.numdam.org/item?id=AIF_2000__50_4_1265_0">Imbalances in Arnoux-Rauzy sequences</a>, Annales de l'institut Fourier, 50 (2000), 1265-1276.
%H A347290 D. Damanik and L. Q. Zamboni, <a href="https://arxiv.org/abs/math/0208137">Arnoux-Rauzy subshifts: linear recurrence, powers and palindromes</a>, arXiv:math/0208137 [math.CO], 2002.
%H A347290 J. Patera, <a href="http://sts-karelia09.jinr.ru/publish/Pepan/v-33-7/20.pdf">Generating the Fibonacci chain in O(log n) space and O(n) time</a> (2003)
%H A347290 Gérard Rauzy, <a href="https://doi.org/10.24033/bsmf.1957">Nombres algébriques et substitutions</a>, Bull. Soc. Math. France 110.2 (1982): 147-178.
%H A347290 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%t A347290 Nest[ Flatten[# /. {0 -> {0, 2, 0, 1, 0, 2, 0}, 1 -> {1, 0, 2, 0}, 2 -> {2, 0, 1, 0, 2, 0}}] &, {0}, 3]
%Y A347290 Cf. A080843 A286998 (values 0,2,1), A058265.
%K A347290 nonn
%O A347290 1,2
%A A347290 _Jiri Hladky_, Aug 29 2021