A049320 Non-primitive Chacon sequence: fixed under 0->0010, 1->1.

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, 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, 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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

A word that is pure morphic and primitive morphic, but neither uniform morphic nor pure primitive morphic. - N. J. A. Sloane, Jul 14 2018

This is A133162 on the alphabet {0,1}, instead of {1,2}. - Michel Dekking, Oct 24 2019

The [10->1]-transform of (a(n)) is the sequence A189640. - Michel Dekking, Oct 26 2019

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10001 [indexing adapted by _Georg Fischer_, Oct 25 2019]
• J.-P. Allouche, M. Baake, J. Cassaigns, and D. Damanik, Palindrome complexity, arXiv:math/0106121 [math.CO], 2001; Theoretical Computer Science, 292 (2003), 9-31.
• Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807 [cs.FL], Nov 29 2017.
• Scott Balchin and Dan Rust, Computations for Symbolic Substitutions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.
• R. V. Chacon, Weakly mixing transformations which are not strongly mixing, Proc. Amer. Math. Soc., 22 (1969), pp. 559-562.
• Fabien Durand, Julien Leroy, and Gwenaël Richomme, Do the Properties of an S-adic Representation Determine Factor Complexity?, Journal of Integer Sequences, Vol. 16 (2013), #13.2.6.
• S. Ferenczi, Complexity of sequences and dynamical systems, Discrete Math., 206 (1999), 145-154.
• Konstantinos Karamanos, Entropy analysis of substitutive sequences revisited, Journal of Physics A: Mathematical and General 34.43 (2001): pages 9231-9241. See Eq. (31).

Crossrefs

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.

Cf. A003849, A049321, A133162, A317962.

Programs

Haskell

a049320 n = a049320_list !! n
a049320_list = 0 : 0 : 1 : 0 : f [0,0,1,0] where
   f xs = drop (length xs) ys ++ f ys where
     ys = concatMap ch xs
     ch 0 = [0,0,1,0]; ch 1 = [1]
-- Reinhard Zumkeller, Aug 14 2013

Mathematica

Nest[# /. 0 -> {0, 0, 1, 0}&, {0}, 4] // Flatten (* Jean-François Alcover, Oct 08 2016 *)

Extensions

Offset changed by Michel Dekking, Oct 24 2019