A287520 - OEIS

A287520

Start with 0 and repeatedly substitute 0->012, 1->102, 2->120.

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

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OFFSET

1,3

COMMENTS

This is the fixed point of the morphism 0->012, 1->102, 2->120 starting with 0. Let u be the (nonperiodic) sequence of positions of 0, and likewise, v for 1 and w for 2; then u(n)/n -> 3, v(n)/n -> 3, w(n)/n -> 3.

It is in fact easy to see that |u(n)-3n|<3, |v(n)-3n|<3, and |w(n)-3n|<3. - Michel Dekking, Oct 02 2019

See A287385 for a guide to related sequences.

LINKS

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

Index entries for sequences that are fixed points of mappings

EXAMPLE

First three iterations of the morphism: 012, 012102120, 012102120102012120102120012.

MATHEMATICA

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287520*)

Flatten[Position[s, 0]]; (* A287521 *)

Flatten[Position[s, 1]]; (* A287522 *)

Flatten[Position[s, 2]]; (* A189630, conjectured *)