A287401 - OEIS

A287401

Start with 0 and repeatedly substitute 0->012, 1->210, 2->120.

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

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OFFSET

1,3

COMMENTS

This is the fixed point of the morphism 0->012, 1->210, 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.

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

FORMULA

a(n) = (2*a(m) + (n-1)*(-1)^a(m)) mod 3, where m = 1 + floor((n-1)/3). - Max Alekseyev, Jul 11 2022

EXAMPLE

First three iterations of the morphism: 012, 012210102, 012210102102210012210012102.

MATHEMATICA

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 1, 0}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287401*)

Flatten[Position[s, 0]]; (*A189728*)

Flatten[Position[s, 1]]; (*A287403*)