A287382 0-limiting word of the mapping 00->1000, 10->001, starting with 00.

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

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

0011000

100010011000

0011000001010011000

1000100110001000001001010011000

0011000001010011000001100010000010001001010011000

The 0-limiting word is the limit of the n-th iterates for even n.

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A287525(n), for n >= 0.

Links

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

Example

The first four n-th iterates for even n:
00
0011000
0011000001010011000
0011000001010011000001100010000010001001010011000

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[23]] - 48   (* A287382 *)
Flatten[Position[st, 0]]  (* A287440 *)
Flatten[Position[st, 1]]  (* A287448 *)
v = Table[StringLength[w[n]], {n, 0, 30}] (* A287525 *)

Crossrefs

Cf. A287440, A287448, A287525, A287530 (1-limiting word).

Sequence in context: A321694 A262684 A373263 * A074290 A091225 A175337

Adjacent sequences: A287379 A287380 A287381 * A287383 A287384 A287385

Keyword

nonn,easy

Author

Clark Kimberling, Jun 18 2017

Status

approved