A288733 1-limiting word of the mapping 00->1000, 10->01, starting with 00.

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

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

011000

01011000

0011011000

10001011011000

011000011011011000

0101100001011011011000

00110110000011011011011000

1000101101100010001011011011011000

The 1-limiting word is the limit of the n-th iterates for n == 1 mod 4. Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288732(n), for n >= 0.

Links

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

Example

The first three n-th iterates for n == 1 mod 3 are
1000
10001011011000
1000101101100010001011011011011000

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "01"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[21]] - 48   (* A288733 *)
Flatten[Position[st, 0]]  (* A288734 *)
Flatten[Position[st, 1]]  (* A288735 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A288732 *)

Crossrefs

Cf. A288729 (0-limiting word), A288734, A288735, A288732, A288736 (2-limiting word), A288741 (3-limiting word).

Sequence in context: A266444 A267679 A267868 * A095111 A166253 A159638

Adjacent sequences: A288730 A288731 A288732 * A288734 A288735 A288736

Keyword

nonn,easy

Author

Clark Kimberling, Jun 16 2017

Status

approved