A284386 Fixed point of the morphism 0->1, 1->1101.

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, 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

Offset

1

Comments

Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (5+sqrt(3))/2 and s = (-1+sqrt(13))/2, so that 1/r + 1/s = 1. Conjecture: 0 < n*r - u(n) < 2 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->1101-> 1101110111101->

Mathematica

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 1, 0, 1}}] &, {0}, 13]; (* A284386 *)
Flatten[Position[s, 0]];  (* A184483 *)
Flatten[Position[s, 1]];  (* A184482 *)

Crossrefs

Cf. A184483, A184482.

Sequence in context: A118828 A105234 A285599 * A286922 A285668 A267813

Adjacent sequences: A284383 A284384 A284385 * A284387 A284388 A284389

Keyword

nonn,easy

Author

Clark Kimberling, Mar 26 2017

Status

approved