A287418 - OEIS

A287418

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

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

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OFFSET

1,3

COMMENTS

This is the fixed point of the morphism 0->012, 1->120, 2->102 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.

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, 012120102, 012120102120102012120012102.

MATHEMATICA

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 2, 0}, 2->{1, 0, 2}}] &, {0}, 9]; (*A287418*)

Flatten[Position[s, 0]]; (*A287419*)

Flatten[Position[s, 1]]; (*A287420*)

Flatten[Position[s, 2]]; (*A287421*)

SubstitutionSystem[{0->{0, 1, 2}, 1->{1, 2, 0}, 2->{1, 0, 2}}, {0}, {5}][[1]] (* Harvey P. Dale, Oct 09 2023 *)