A283963 Fixed point of the morphism 0 -> 1, 1 -> 1010.

1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 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: -1 < n*r - u(n) < 2 and -1 < n*s - v(n) < 2 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 -> 1010 -> 1010110101 -> 1010110101101010101101011010 ->

Mathematica

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 0}}] &, {0}, 10] (* A283963 *)
Flatten[Position[s, 0]]  (* A283964 *)
Flatten[Position[s, 1]]  (* A283965 *)

Crossrefs

Cf. A283964, A283965.

Sequence in context: A113704 A341150 A244220 * A131670 A188044 A287523

Adjacent sequences: A283960 A283961 A283962 * A283964 A283965 A283966

Keyword

nonn,easy

Author

Clark Kimberling, Mar 25 2017

Status

approved