A284369 Fixed point of the morphism 0->1, 1->1001.

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

Offset

1

Comments

Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (3+sqrt(3))/2 and s = sqrt(3), so that 1/r + 1/s = 1. Conjecture: -3 < n*r - u(n) < 4 and -2 < n*s - v(n) < 3 for n >= 1.

Links

Clark Kimberling, Table of n, a(n) for n = 1..31647

Index entries for sequences that are fixed points of mappings

Example

1->1001-> 1001111001->

Mathematica

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 0, 1}}] &, {0}, 15]; (* A284369 *)
Flatten[Position[s, 0]];  (* A284370 *)
Flatten[Position[s, 1]];  (* A284371 *)

Crossrefs

Cf. A284370, A284371.

Sequence in context: A168394 A072770 A090172 * A194661 A373136 A285427

Adjacent sequences: A284366 A284367 A284368 * A284370 A284371 A284372

Keyword

nonn,easy

Author

Clark Kimberling, Mar 26 2017

Status

approved