A285258 1-limiting word of the morphism 0->10, 1-> 0110.

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

Offset

1

Comments

The morphism 0->10, 1-> 0110 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 011010 -> 100110011010011010 -> 011010100110011010100110011010011010100110011010011010; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 011010 -> 100110011010011010, as in A285258.

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, 1, 0}}] &, {0}, 11]; (* A285258 *)
Flatten[Position[s, 0]];  (* A285259 *)
Flatten[Position[s, 1]];  (* A285260 *)

Crossrefs

Cf. A285255, A285259, A285260.

Sequence in context: A102560 A190669 A355328 * A068428 A373155 A078650

Adjacent sequences: A285255 A285256 A285257 * A285259 A285260 A285261

Keyword

nonn,easy

Author

Clark Kimberling, Apr 24 2017

Status

approved