A287386 -id:A287386

The OEIS is supported by the many generous donors to the OEIS Foundation.

Search: a287386 -id:a287386

Displaying 1-3 of 3 results found.

page 1

A287385

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

+10
19

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

(list; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 25 2017

EXTENSIONS

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

STATUS

approved

A287387

Positions of 1 in A287385.

+10
4

2, 5, 9, 12, 14, 17, 20, 24, 26, 29, 33, 35, 39, 41, 44, 47, 50, 54, 56, 59, 63, 65, 69, 71, 75, 77, 80, 83, 86, 90, 92, 96, 98, 102, 104, 107, 110, 114, 116, 120, 122, 125, 128, 131, 135, 137, 140, 144, 147, 149, 152, 155, 159, 161, 164, 167, 171, 174, 176

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) - a(n-1) is in {2,3,4} for n >= 1; also, 3n - a(n) is in {0,1} for n >= 1. The first 20 numbers 3n - a(n) are 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, with 0 in positions given by A287388.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

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. A287385, A287386, A287388.

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 25 2017

STATUS

approved

A287388

Positions of 2 in A287385.

+10
4

3, 4, 8, 11, 13, 18, 21, 23, 25, 30, 32, 34, 38, 40, 45, 48, 49, 53, 57, 58, 62, 66, 68, 70, 74, 76, 81, 84, 85, 89, 93, 95, 97, 101, 103, 108, 111, 113, 115, 119, 121, 126, 129, 130, 134, 138, 139, 143, 146, 148, 153, 156, 158, 160, 165, 166, 170, 173, 175

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) - a(n-1) is in {1,2,3,4,5} for n >= 1; also, 3n - a(n) is in {0,1,2} for n >= 1. The first 20 numbers 3n - a(n) are 0, 2, 1, 1, 2, 0, 0, 1, 2, 0, 1, 2, 1, 2, 0, 0, 2, 1, 0, 2, with 0 in positions given by A287386.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

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. A287385, A287386, A287387.

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 25 2017

STATUS

approved

page 1

Search completed in 0.007 seconds