A284364 Fixed point of the morphism 0->1, 1->101010.

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

Offset

1

Comments

Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (9+sqrt(21))/6 and s = (-1+sqrt(21))/2, so that 1/r + 1/s = 1. Conjecture: -2 < 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->101010-> 101010110101011010101->

Mathematica

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 0, 1, 0}}] &, {0}, 10] (* A284364 *)
Flatten[Position[s, 0]]  (* A284365 *)
Flatten[Position[s, 1]]  (* A284366 *)

Crossrefs

Cf. A284365, A284366.

Sequence in context: A191188 A285592 A276793 * A115788 A195062 A351077

Adjacent sequences: A284361 A284362 A284363 * A284365 A284366 A284367

Keyword

nonn,easy

Author

Clark Kimberling, Mar 26 2017

Status

approved