A285159 0-limiting word of the morphism 0->10, 1-> 0011.

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

Clark Kimberling, Table of n, a(n) for n = 1..10000

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

Cf. A285160, A285161, A285162.

Sequence in context: A138150 A271591 A287790 * A073089 A373470 A373141

Adjacent sequences: A285156 A285157 A285158 * A285160 A285161 A285162

Keyword

nonn,easy

Author

Clark Kimberling, Apr 21 2017

Status

approved