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A287086 Start with 0 and repeatedly substitute 0->01, 1->22, 2->0. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 15:40 EDT 2017. Contains 293620 sequences.