A285252 1-limiting word of the morphism 0->10, 1-> 0101.

1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0

Offset

1

Comments

The morphism 0->10, 1-> 0101 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 0101 -> 100101100101 -> 010110100101100101010110100101100101; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 0101 -> 100101100101, as in A285252.

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, 1, 0, 1}}] &, {0}, 11]; (* A285252 *)
Flatten[Position[s, 0]];  (* A285253 *)
Flatten[Position[s, 1]];  (* A285254 *)

Crossrefs

Cf. A285250, A285253, A285254.

Sequence in context: A365410 A373549 A181406 * A076404 A317961 A010059

Adjacent sequences: A285249 A285250 A285251 * A285253 A285254 A285255

Keyword

nonn,easy

Author

Clark Kimberling, Apr 23 2017

Status

approved