login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A287337 0-limiting word of the morphism 0->11, 1->20, 2->0. 6
0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

Starting with 0, the first 5 iterations of the morphism yield words shown here:

1st:  11

2nd:  2020

3rd:  011011

4th:  112020112020

5th:  20200110112020011011

The 0-limiting word is the limit of the words for which the number of iterations congruent to 0 mod 3.

Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively.  Then 1/U + 1/V + 1/W = 1, where

U = 2.7692923542386314152404094643350334926...,

V = 2.4498438945029551040577327454145475624...,

W = 4.3344900716222708116779374775820643087...

If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,5,6,10}, and w(n) - w(n-1) is in {2,4,8,10,16}.

LINKS

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

EXAMPLE

3rd iterate: 011011

6th iterate: 011011112020112020011011112020112020

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 12] (* A287337 *)

Flatten[Position[s, 0]] (* A287338 *)

Flatten[Position[s, 1]] (* A287339 *)

Flatten[Position[s, 2]] (* A287340 *)

CROSSREFS

Cf. A287338, A287339, A287340, A287341 (1-limiting word), A287345 (2-limiting word).

Sequence in context: A112712 A026608 A264049 * A026612 A287341 A282432

Adjacent sequences:  A287334 A287335 A287336 * A287338 A287339 A287340

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 24 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 24 17:01 EDT 2019. Contains 326295 sequences. (Running on oeis4.)