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Primitive Chacon sequence: fixed under 0->0012, 1->12, 2->012.
3

%I #31 Dec 03 2020 02:52:22

%S 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,

%T 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,

%U 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

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

%C 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

%H Reinhard Zumkeller, <a href="/A049321/b049321.txt">Table of n, a(n) for n = 0..10000</a>

%H Scott Balchin and Dan Rust, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Rust/rust3.html">Computations for Symbolic Substitutions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.

%H S. Ferenczi, <a href="https://doi.org/10.24033/bsmf.2260">Les transformations de Chacon: combinatoire, structure géométrique, lien avec les systèmes de complexité 2n+1</a>, Bull. Soc. Math. France 123 (1995), 271-292.

%H S. Ferenczi, <a href="http://dx.doi.org/10.1016/S0012-365X(98)00400-2">Complexity of sequences and dynamical systems</a>, Discrete Math., 206 (1999), 145-154.

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%F 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

%e beta(0001000...) = beta(00)beta(00)beta(01)beta(10)beta(00)beta(00)... = 001200.... - _Michel Dekking_, Oct 24 2019

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

%o (Haskell)

%o a049321 n = a049321_list !! n

%o a049321_list = 0 : 0 : 1 : 2 : f [0,0,1,2] where

%o f xs = drop (length xs) ys ++ f ys where

%o ys = concatMap ch xs

%o ch 0 = [0,0,1,2]; ch 1 = [1,2]; ch 2 = [0,1,2]

%o -- _Reinhard Zumkeller_, Aug 14 2013

%Y Cf. A003849, A049320.

%K nonn,nice,easy

%O 0,4

%A _N. J. A. Sloane_

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