A287407 - OEIS

A287407

Start with 0 and repeatedly substitute 0->012, 1->210, 2->201.

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

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OFFSET

1,3

COMMENTS

This is the fixed point of the morphism 0->012, 1->210, 2->201 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, 012210201, 012210201201210012201012210.

MATHEMATICA

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 1, 0}, 2->{2, 0, 1}}] &, {0}, 9]; (*A287407*)

Flatten[Position[s, 0]]; (*A287408*)

Flatten[Position[s, 1]]; (*A287409*)

Flatten[Position[s, 2]]; (*A287410*)

SubstitutionSystem[{0->{0, 1, 2}, 1->{2, 1, 0}, 2->{2, 0, 1}}, 0, {5}][[1]] (* Harvey P. Dale, Aug 03 2023 *)