A049321 Primitive Chacon sequence: fixed under 0->0012, 1->12, 2->012.

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

Offset

0,4

Comments

This sequence was introduced by Ferenczi in his 1995 paper. It has the property that it maps to the non-primitive Chacon sequence A049320 via the letter-to-letter map 0->0, 1->1, 2->0. See Ferenczi's paper, page 281. - Michel Dekking, Oct 24 2019

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Scott Balchin and Dan Rust, Computations for Symbolic Substitutions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.

S. Ferenczi, Les transformations de Chacon: combinatoire, structure géométrique, lien avec les systèmes de complexité 2n+1, Bull. Soc. Math. France 123 (1995), 271-292.

S. Ferenczi, Complexity of sequences and dynamical systems, Discrete Math., 206 (1999), 145-154.

Index entries for sequences that are fixed points of mappings

Formula

a(n) = beta(0 A049320(n)), where beta is the 2-block map given by 00->0, 10->2, 01->1. - Michel Dekking, Oct 24 2019

Example

beta(0001000...) = beta(00)beta(00)beta(01)beta(10)beta(00)beta(00)... = 001200.... - Michel Dekking, Oct 24 2019

Mathematica

Nest[Flatten[# /. {0 -> {0, 0, 1, 2}, 1 -> {1, 2}, 2 -> {0, 1, 2}}]&, {0}, 4] (* Jean-François Alcover, Oct 05 2016 *)

Prog

(Haskell)
a049321 n = a049321_list !! n
a049321_list = 0 : 0 : 1 : 2 : f [0, 0, 1, 2] where
   f xs = drop (length xs) ys ++ f ys where
     ys = concatMap ch xs
     ch 0 = [0, 0, 1, 2]; ch 1 = [1, 2]; ch 2 = [0, 1, 2]
-- Reinhard Zumkeller, Aug 14 2013

Crossrefs

Cf. A003849, A049320.

Sequence in context: A024942 A210255 A283319 * A204425 A245187 A292598

Adjacent sequences: A049318 A049319 A049320 * A049322 A049323 A049324

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2000

Status

approved