OFFSET
1,1
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
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).
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.
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Offset changed by Michel Dekking, Oct 24 2019
STATUS
approved