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A285159
0-limiting word of the morphism 0->10, 1-> 0011.
6
0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1
OFFSET
1
COMMENTS
The morphism 0->10, 1-> 0011 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 001110 -> 101000110011001110 -> 001110001110101000110011101000110011101000110011001110; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 001110 -> 101000110011001110, as in A285162.
This is a 3-automatic sequence. See Allouche et al. link. - Michel Dekking, Oct 05 2020
LINKS
J.-P. Allouche, F. M. Dekking, and M. Queffélec, Hidden automatic sequences, arXiv:2010.00920 [math.NT], 2020.
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 0, 1, 1}}] &, {0}, 10]; (* A285159 *)
Flatten[Position[s, 0]]; (* A285160 *)
Flatten[Position[s, 1]]; (* A285161 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 21 2017
STATUS
approved