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A049320 Nonprimitive Chacon sequence: fixed under 0->0010, 1->1. 26
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

LINKS

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

J.-P. Allouche, M. Baake, J. Cassaigns and D. Damanik, Palindrome complexity, arXiv:math/0106121 [math.CO], 2001.

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).

FORMULA

Cf. A003849, A049321.

MATHEMATICA

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

PROG

(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

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. A317962.

Sequence in context: A289165 A156729 A188079 * A284817 A284524 A226474

Adjacent sequences:  A049317 A049318 A049319 * A049321 A049322 A049323

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 21 11:21 EST 2019. Contains 319354 sequences. (Running on oeis4.)