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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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

Examples

			beta(0001000...) = beta(00)beta(00)beta(01)beta(10)beta(00)beta(00)... = 001200.... - _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

Crossrefs

Cf. A003849, A049320.

Programs

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

Mathematica

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

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

Extensions

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