A285249 0-limiting word of the morphism 0->10, 1-> 0101.

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, 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.

Links

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

Michel Rigo, Manon Stipulanti, and Markus A. Whiteland, Automatic Abelian Complexities of Parikh-Collinear Fixed Points, arXiv:2405.18032 [cs.DM], 2024. See page 2.

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 1, 0, 1}}] &, {0}, 12]; (* A285249 *)
Flatten[Position[s, 0]];  (* A285250 *)
Flatten[Position[s, 1]];  (* A285251 *)

Crossrefs

Cf. A285250, A285251, A285252.

Sequence in context: A291291 A324681 A368909 * A269027 A089809 A165211

Adjacent sequences: A285246 A285247 A285248 * A285250 A285251 A285252

Keyword

nonn,easy

Author

Clark Kimberling, Apr 23 2017

Status

approved