A284505 Fixed point of the morphism 0->1, 1->1100.

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, 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

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) < 4 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

0-> 1-> 1100-> 1100110011-> ...

Mathematica

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 1, 0, 0}}] &, {0}, 16]; (* A284505 *)
Flatten[Position[s, 0]];  (* A284506 *)
Flatten[Position[s, 1]];  (* A284507 *)

Crossrefs

Cf. A284506, A284507.

Sequence in context: A286903 A339052 A284490 * A285661 A265698 A267673

Adjacent sequences: A284502 A284503 A284504 * A284506 A284507 A284508

Keyword

nonn,easy

Author

Clark Kimberling, Apr 04 2017

Status

approved