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Search: id:A103269
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| A103269 |
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a(n) = concatenation of n-th stage of the trajectory of 1 under the tribonacci morphism 1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1}. |
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3
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| 1, 12, 1213, 1213121, 1213121121312, 121312112131212131211213, 12131211213121213121121312131211213121213121, 12131211213121213121121312131211213121213121121312112131212131211213121312112131\ 2
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A092782 is the official version of this sequence. - N. J. A. Sloane (njas(AT)research.att.com), Oct 03 2007
In a 1982 paper Rauzy showed that the subshift (X, T) generated by the morphism 1 -> 12, 2 -> 13 and 3 -> 1 is a natural coding of a rotation on the two-dimensional torus T^2, i.e. is measure-theoretically conjugate (metrically isomorphic) to an exchange of three fractal domains on a compact set in R^2 each domain being translated by the same vector modulo a lattice.
The number of letters in the n-th iteration is tribonacci(n).
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REFERENCES
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David Damanik and Luca Q. Zamboni, Arnoux-Rauzy Subshifts: Linear Recurrence, Powers and Palindromes, math.CO/0208137.
S. Ito and M. Kimura, On Rauzy fractal, Japan J. Indust. Appl. Math. 8 (1991) 461-486.
A. Messaoudi, Proprietes arithmetiques et dynamiques du fractal de Rauzy, J. Th. Nombres Bordeaux, 10 (1998) 195-224.
Gerard Rauzy, Nombres algebriques et substitutions, Bull. Soc. Math. France, 110 (1982), 147-178.
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LINKS
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Cassaigne, Julien; Ferenczi, Sebastien; and Zamboni, Luca Q., Imbalances in Arnoux-Rauzy sequences, Annales de l'institut Fourier, 50 (2000), 1265-1276.
C. Holton and L. Q. Zamboni, Directed Graphs and Substitutions, Theory Comput. Systems, 34 (2001) 545-564
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MATHEMATICA
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FromDigits /@ NestList[ Flatten[ # /. {1 -> {1, 2}, 2 -> {1, 3}, 3 -> 1}] &, {1}, 7]
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CROSSREFS
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Cf. A106748, A106749, A003842, A106750, A092782.
Sequence in context: A112457 A091782 A112580 this_sequence A033564 A054351 A080814
Adjacent sequences: A103266 A103267 A103268 this_sequence A103270 A103271 A103272
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), May 16 2005
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