login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288670 1-limiting word of the mapping 00->0110, 10->000, starting with 00. 4
0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates of the mapping, starting with 00:

00

0110

01000

00000110

0110011001000

010000100000000110

00000110000001100110011001000

01100110010000110011001000010000100000000110

The 1-limiting word is the limit of the n-th iterates for n == 1 mod 3. Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288468(n).

LINKS

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

EXAMPLE

The first three n-th iterates for n == 1 mod 3 are

0110

0110011001000

01100110010000110011001000010000100000000110

MATHEMATICA

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "000"}]

Table[w[n], {n, 0, 8}]

st = ToCharacterCode[w[13]] - 48   (* A288670 *)

Flatten[Position[st, 0]]  (* A288671 *)

Flatten[Position[st, 1]]  (* A288672 *)

CROSSREFS

Cf. A288665 (0-limiting word), A288671, A288672, A288673 (2-limiting word).

Sequence in context: A286049 A287657 A079336 * A057215 A284905 A291197

Adjacent sequences:  A288667 A288668 A288669 * A288671 A288672 A288673

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 15 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 September 25 23:58 EDT 2021. Contains 347664 sequences. (Running on oeis4.)