A288551 0-limiting word of the mapping 00->0101, 1->011, starting with 00.

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

Offset

1

Comments

Iterates, starting with 00:

00

0101

00110011

01010110110101011011

00110011001101100110110011001100110110011011

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 A288476(n).

Links

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

Example

First three even-numbered iterates of the mapping:
00
00110011
00110011001101100110110011001100110110011011

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[10]] - 48   (* A288551 *)
Flatten[Position[st, 0]]  (* A288552 *)
Flatten[Position[st, 1]]  (* A288553 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288476 conjectured *)

Crossrefs

Cf. A288552, A288553, A288476, A288473 (the 1-limiting word).

Sequence in context: A132380 A021913 A285501 * A327174 A269723 A284487

Adjacent sequences: A288548 A288549 A288550 * A288552 A288553 A288554

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 2017

Status

approved