A287385 Start with 0 and repeatedly substitute 0->012, 1->210, 2->021.

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

Offset

1,3

Comments

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

In the following guide to related sequences, column 1 indexes fixed points on {1,2,3}, and columns 2,3,4 match the position sequences of 0, 1, 2. Those sequences therefore comprise a 3-way splitting of the positive integers.

Fixed point and morphism Position sequences

A287385: 0->012, 1->210, 2->021 A287386 A287387 A287388

A287397: 0->012, 1->210, 2->102 A287398 A287399 A287400

A287401: 0->012, 1->210, 2->120 A189728 A287403 A287404

A287407: 0->012, 1->210, 2->201 A287408 A287409 A287410

A287411: 0->012, 1->120, 2->021 A287412 A287413 A287414

A287418: 0->012, 1->120, 2->102 A287419 A287420 A287421

A053838: 0->012, 1->120, 2->201 A287435 A287436 A287437

A287438: 0->012, 1->120, 2->210 A189728 A189670 A287441

A287443: 0->012, 1->201, 2->021 A287444 A287445 A287446

A287447: 0->012, 1->201, 2->102 A189724 A287449 A287450

A287451: 0->012, 1->201, 2->120 A287452 A287453 A287454

A287455: 0->012, 1->201, 2->210 A287456 A189666 A287458

A287516: 0->012, 1->102, 2->021 A287517 A287518 A189630

A287520: 0->012, 1->102, 2->120 A287521 A287522 A189630

A287524: 0->012, 1->102, 2->201 A189724 A287526 A287527

A287528: 0->012, 1->102, 2->210 A287529 A189670 A189634

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, 012210021, 012210021021210012012021210.

Mathematica

s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 1, 0}, 2->{0, 2, 1}}] &, {0}, 9]; (*A287385*)
Flatten[Position[s, 0]]; (*A287386*)
Flatten[Position[s, 1]]; (*A287387*)
Flatten[Position[s, 2]]; (*A287388*)

Crossrefs

Cf. A287386, A287387, A287388.

Sequence in context: A258747 A160806 A344447 * A191411 A133418 A181169

Adjacent sequences: A287382 A287383 A287384 * A287386 A287387 A287388

Keyword

nonn,easy

Author

Clark Kimberling, May 25 2017

Extensions

Two entries in overview corrected by Georg Fischer, Sep 20 2021

Status

approved