A288520 0-limiting word of the mapping 00->0101, 10->010, starting with 00.

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

Offset

1

Comments

Iterates, starting with 00:

00

0101

00101

01010101

00100100101

0101010001000101

0010010010010101001010101

010101000100010001001001000100100101

The 0-limiting word is the limit taken over even-numbered iterations of the mapping.

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288523(n).

Links

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

Example

The first 4 even-numbered iterates:
00
00101
00100100101
0010010010010101001010101

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "010"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[18]] - 48   (* A288520 *)
Flatten[Position[st, 0]]  (* A288521 *)
Flatten[Position[st, 1]]  (* A288522 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288523 conjectured *)

Crossrefs

Cf. A288521, A288522, A288523.

Sequence in context: A353514 A144604 A022926 * A285177 A144595 A340507

Adjacent sequences: A288517 A288518 A288519 * A288521 A288522 A288523

Keyword

nonn,easy

Author

Clark Kimberling, Jun 13 2017

Status

approved