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.

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, 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, 2, 0, 1, 0, 2, 0, 0

Offset

1,2

Comments

Arnoux-Rauzy word sigma_0 x sigma_2 x sigma_1, where sigmas are defined as:

sigma_0 : 0 -> 0, 1 -> 10, 2 -> 20;

sigma_1 : 0 -> 01, 1 -> 1, 2 -> 21;

sigma_2 : 0 -> 02, 1 -> 12, 2 -> 2.

Fixed point of the morphism 0->0201020, 1->1020, 2->201020 starting from a(1)=0.

Frequency of letters:

0: 1/t ~ 54.368% (A192918)

1: 1/t^3 ~ 16.071%

2: 1/t^2 ~ 29.559%

where t is tribonacci constant A058265.

Equals A286998 with a re-mapping of values 1->2, 2->1.

Links

Table of n, a(n) for n=1..75.

L. Balková, M. Bucci, A. De Luca, J. Hladký and S. Puzynina, Aperiodic Pseudorandom Number Generators Based on Infinite Words, Theoret. Comput. Sci. 647 (2016), 85-100.

Julien Cassaigne, Sebastien Ferenczi, and Luca Q. Zamboni, Imbalances in Arnoux-Rauzy sequences, Annales de l'institut Fourier, 50 (2000), 1265-1276.

D. Damanik and L. Q. Zamboni, Arnoux-Rauzy subshifts: linear recurrence, powers and palindromes, arXiv:math/0208137 [math.CO], 2002.

J. Patera, Generating the Fibonacci chain in O(log n) space and O(n) time (2003)

Gérard Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France 110.2 (1982): 147-178.

Index entries for sequences that are fixed points of mappings

Mathematica

Nest[ Flatten[# /. {0 -> {0, 2, 0, 1, 0, 2, 0}, 1 -> {1, 0, 2, 0}, 2 -> {2, 0, 1, 0, 2, 0}] &, {0}, 8]

Crossrefs

Cf. A080843 A286998 (values 0,2,1), A058265.

Sequence in context: A286351 A091394 A029881 * A070090 A230642 A053473

Adjacent sequences: A347287 A347288 A347289 * A347291 A347292 A347293

Keyword

nonn

Author

Jiri Hladky, Aug 29 2021

Status

approved