A288524 1-limiting word of the mapping 00->0101, 10->010, starting with 00.

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

Offset

1

Comments

Iterates, starting with 00:

00

0101

00101

01010101

00100100101

0101010001000101

0010010010010101001010101

010101000100010001001001000100100101

The 1-limiting word is the limit taken over odd-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 odd-numbered iterates:
0101
01010101
0101010001000101
010101000100010001001001000100100101

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[19]] - 48   (* A288524 *)
Flatten[Position[st, 0]]  (* A288525 *)
Flatten[Position[st, 1]]  (* A288526 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288523 conjectured *)

Crossrefs

Cf. A288525, A288526, A288523.

Sequence in context: A141743 A268384 A358670 * A112416 A061265 A288466

Adjacent sequences: A288521 A288522 A288523 * A288525 A288526 A288527

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 2017

Status

approved