A284368 Fixed point of the morphism 0->1, 1->1011.

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

Offset

1

Comments

Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (5+sqrt(13))/2 and s = (-1+sqrt(13))/2, so that 1/r + 1/s = 1. Conjecture: 1 < n*r - u(n) < 3 and -1 < n*s - v(n) < 1 for n >= 1.

Links

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

Index entries for sequences that are fixed points of mappings

Example

1->1011-> 1011110111011->

Mathematica

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 1}}] &, {0}, 10] (* A284368 *)
Flatten[Position[s, 0]]  (* A184485 *)
Flatten[Position[s, 1]]  (* A184484 *)

Crossrefs

Cf. A184484, A184485.

Sequence in context: A121967 A356310 A285430 * A287725 A176702 A188038

Adjacent sequences: A284365 A284366 A284367 * A284369 A284370 A284371

Keyword

nonn,easy

Author

Clark Kimberling, Mar 26 2017

Status

approved