A288512 1-limiting word of the mapping 00->0101, 10->001, starting with 00.

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

Offset

1

Comments

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288511(n).

Iterates, starting with 00:

00

0101

00011

0101011

000100111

010100010111

00010010101001111

01010001000100100101111

000100101010010101001000100011111

The 1-limiting word is the limit taken over odd-numbered iterations of the mapping.

Links

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

Example

The first 4 odd-numberd iterates:
0101
0101011
010100010111
01010001000100100101111

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[19]] - 48   (* A288512 *)
Flatten[Position[st, 0]]  (* A288513 *)
Flatten[Position[st, 1]]  (* A288514 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288511 conjectured *)

Crossrefs

Cf. A288511, A288513, A288514.

Sequence in context: A353811 A116865 A353674 * A157687 A189668 A353525

Adjacent sequences: A288509 A288510 A288511 * A288513 A288514 A288515

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2017

Status

approved