A287457 1-limiting word of the mapping 00->1000, 10->000, starting with 00.

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

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

0001000

100000001000

0001000100010000001000

10000000100000010000001000100000001000

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 A287439(n), for n >= 0.

See comments of A287372 for a proof of this conjecture. - Michel Dekking, Mar 19 2018

Links

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

Example

The first three n-th iterates for odd n:
1000
100000001000
10000000100000010000001000100000001000

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "000"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[23]] - 48   (* A287457 *)
Flatten[Position[st, 0]]  (* A287519 *)
Flatten[Position[st, 1]]  (* A287186 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A287439 *)

Crossrefs

Cf. A287372 (0-limiting word), A287519, A287186, A287439.

Sequence in context: A253513 A014025 A279760 * A358777 A359595 A353557

Adjacent sequences: A287454 A287455 A287456 * A287458 A287459 A287460

Keyword

nonn,easy

Author

Clark Kimberling, Jun 17 2017

Status

approved