A287530 1-limiting word of the mapping 00->1000, 10->001, starting with 00.

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

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

0011000

100010011000

0011000001010011000

1000100110001000001001010011000

0011000001010011000001100010000010001001010011000

The 1-limiting word is the limit of the n-th iterates for odd 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 three n-th iterates for even n:
1000
100010011000
1000100110001000001001010011000

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   (* A287530 *)
Flatten[Position[st, 0]]  (* A287531 *)
Flatten[Position[st, 1]]  (* A287551 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A287525 *)

Crossrefs

Cf. A287382 (0-limiting word), A287531, A287551, A287525.

Sequence in context: A102243 A173859 A202108 * A104108 A267056 A089024

Adjacent sequences: A287527 A287528 A287529 * A287531 A287532 A287533

Keyword

nonn,easy

Author

Clark Kimberling, Jun 18 2017

Status

approved