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%I #67 Feb 05 2023 09:10:19
%S 0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,0,1,
%T 0,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0,1,0,1,0,
%U 0,1,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,1,0,0
%N Non-primitive Chacon sequence: fixed under 0->0010, 1->1.
%C A word that is pure morphic and primitive morphic, but neither uniform morphic nor pure primitive morphic. - _N. J. A. Sloane_, Jul 14 2018
%C This is A133162 on the alphabet {0,1}, instead of {1,2}. - _Michel Dekking_, Oct 24 2019
%C The [10->1]-transform of (a(n)) is the sequence A189640. - _Michel Dekking_, Oct 26 2019
%H Reinhard Zumkeller, <a href="/A049320/b049320.txt">Table of n, a(n) for n = 1..10001</a> [indexing adapted by _Georg Fischer_, Oct 25 2019]
%H J.-P. Allouche, M. Baake, J. Cassaigns, and D. Damanik, <a href="http://arxiv.org/abs/math/0106121">Palindrome complexity</a>, arXiv:math/0106121 [math.CO], 2001; <a href="http://dx.doi.org/10.1016/S0304-3975(01)00212-2">Theoretical Computer Science</a>, 292 (2003), 9-31.
%H Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, <a href="https://arxiv.org/abs/1711.10807">A Taxonomy of Morphic Sequences</a>, arXiv preprint arXiv:1711.10807 [cs.FL], Nov 29 2017.
%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 R. V. Chacon, <a href="https://doi.org/10.1090/S0002-9939-1969-0247028-5">Weakly mixing transformations which are not strongly mixing</a>, Proc. Amer. Math. Soc., 22 (1969), pp. 559-562.
%H Fabien Durand, Julien Leroy, and Gwenaël Richomme, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Durand/durand2.html">Do the Properties of an S-adic Representation Determine Factor Complexity?</a>, Journal of Integer Sequences, Vol. 16 (2013), #13.2.6.
%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 Konstantinos Karamanos, <a href="https://www.researchgate.net/publication/230903001_Entropy_analysis_of_substitutive_sequences_revisited">Entropy analysis of substitutive sequences revisited</a>, Journal of Physics A: Mathematical and General 34.43 (2001): pages 9231-9241. See Eq. (31).
%t Nest[# /. 0 -> {0, 0, 1, 0}&, {0}, 4] // Flatten (* _Jean-François Alcover_, Oct 08 2016 *)
%o (Haskell)
%o a049320 n = a049320_list !! n
%o a049320_list = 0 : 0 : 1 : 0 : f [0,0,1,0] where
%o f xs = drop (length xs) ys ++ f ys where
%o ys = concatMap ch xs
%o ch 0 = [0,0,1,0]; ch 1 = [1]
%o -- _Reinhard Zumkeller_, Aug 14 2013
%Y Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.
%Y Cf. A003849, A049321, A133162, A317962.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_
%E Offset changed by _Michel Dekking_, Oct 24 2019
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