A285083 1-limiting word of the morphism 0->10, 1-> 011.

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

Offset

1

Comments

The morphism 0->10, 1->011 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 01110 -> 1001101101110 -> 0111010011011100110111001101101110, as in A285080; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 01110 -> 1001101101110, as in A285083.

Let v(n) = position of n-th 1. Then v(n)/n -> (1+sqrt(5))/2, the golden ratio (A001622); see A285082.

Links

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

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 1, 1}}] &, {0}, 13]; (* A285083 *)
Flatten[Position[s, 0]];  (* A285084 *)
Flatten[Position[s, 1]];  (* A285085 *)

Crossrefs

Cf. A001622, A285080, A285084, A285085.

Sequence in context: A187074 A188398 A288929 * A266982 A364746 A051341

Adjacent sequences: A285080 A285081 A285082 * A285084 A285085 A285086

Keyword

nonn,easy

Author

Clark Kimberling, Apr 19 2017

Status

approved