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A288220 1-limiting word of the mapping 00->1000, 10->010, starting with 00. 5
1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 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

1000

0101000

00100101000

100001000100101000

01010000010100001000100101000

00100101000100001001010000010100001000100101000

The 1-limiting word is the limit of the n-th iterates for n == 1 mod 3.

The number of letters (0's and 1's) in the n-th iterate is given by A288219(n), for n >= 0.

LINKS

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

EXAMPLE

The first two n-th iterates for n == 1 mod 3:

1000

100001000100101000

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "010"}]

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

st = ToCharacterCode[w[22]] - 48   (* A288220 *)

Flatten[Position[st, 0]]  (* A288221 *)

Flatten[Position[st, 1]]  (* A288222 *)

Table[StringLength[w[n]], {n, 0, 30}] (* A288219 *)

CROSSREFS

Cf. A288216 (0-limiting word), A288221, A288222, A288219, A288223 (2-limiting word).

Sequence in context: A339661 A320656 A322075 * A173856 A288926 A027356

Adjacent sequences:  A288217 A288218 A288219 * A288221 A288222 A288223

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 19 2017

STATUS

approved

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Last modified May 11 09:11 EDT 2021. Contains 343788 sequences. (Running on oeis4.)