A287086 Start with 0 and repeatedly substitute 0->01, 1->22, 2->0.

0, 1, 2, 2, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2

Offset

1,3

Comments

The fixed point of the morphism 0->01, 1->20, 2->1. Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2. Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively. Then 1/U + 1/V + 1/W = 1, where

U = 2.28537528186132044169516884721360670506...,

V = 3.87512979416277882597397059430967806752...,

W = 3.28537528186132044169516884721360670506...

If n >=2, then u(n) - u(n-1) is in {1,2,4}, v(n) - v(n-1) is in {2,4,6}, and w(n) - w(n-1) is in {1,3,5,9}.

Links

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

Index entries for sequences that are fixed points of mappings

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 10] (* A287086 *)
Flatten[Position[s, 0]] (* A287087 *)
Flatten[Position[s, 1]] (* A287088 *)
Flatten[Position[s, 2]] (* A287089 *)

Crossrefs

Cf. A287087, A287088, A287089.

Sequence in context: A113302 A292946 A196078 * A180823 A049800 A281082

Adjacent sequences: A287083 A287084 A287085 * A287087 A287088 A287089

Keyword

nonn,easy

Author

Clark Kimberling, May 21 2017

Status

approved