A288473 1-limiting word of the mapping 00->0101, 1->011, starting with 00.

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

Offset

1

Comments

Iterates, starting with 00:

00

0101

00110011

01010110110101011011

00110011001101100110110011001100110110011011

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 A288476(n).

Links

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

Example

First two odd-numbered iterates of the mapping:
0101
01010110110101011011

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "1" -> "011"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288473 *)
Flatten[Position[st, 0]]  (* A288474 *)
Flatten[Position[st, 1]]  (* A288475 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288476 conjectured *)

Crossrefs

Cf. A288474, A288475, A288476, A288551 (0-limiting word).

Sequence in context: A082446 A191156 A144611 * A130853 A353810 A115516

Adjacent sequences: A288470 A288471 A288472 * A288474 A288475 A288476

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2017

Status

approved