A288223 2-limiting word of the mapping 00->1000, 10->010, starting with 00.

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, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 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, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

0101000

00100101000

100001000100101000

01010000010100001000100101000

00100101000100001001010000010100001000100101000

The 2-limiting word is the limit of the n-th iterates for n == 2 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:
0101000
01010000010100001000100101000

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[20]] - 48   (* A288223 *)
Flatten[Position[st, 0]]  (* A288224 *)
Flatten[Position[st, 1]]  (* A288225 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288219 *)

Crossrefs

Cf. A288216 (0-limiting word), A288220 (1-limiting word), A288224, A288225, A288219.

Sequence in context: A071674 A179829 A172486 * A353811 A116865 A353674

Adjacent sequences: A288220 A288221 A288222 * A288224 A288225 A288226

Keyword

nonn,easy

Author

Clark Kimberling, Jun 19 2017

Status

approved