A287443 Start with 0 and repeatedly substitute 0->012, 1->201, 2->021.

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

Offset

1,3

Comments

This is the fixed point of the morphism 0->012, 1->201, 2->021 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, 012201021, 012201021021012201012021201.

Mathematica

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 0, 1}, 2->{0, 2, 1}}] &, {0}, 9]; (*A287443*)
Flatten[Position[s, 0]]; (*A287444*)
Flatten[Position[s, 1]]; (*A287445*)
Flatten[Position[s, 2]]; (*A287446*)

Crossrefs

Cf. A287385, A287444, A287445, A287446.

Sequence in context: A377415 A113685 A049825 * A039651 A264403 A038190

Adjacent sequences: A287440 A287441 A287442 * A287444 A287445 A287446

Keyword

nonn,easy

Author

Clark Kimberling, May 26 2017

Status

approved