A289025 Fixed point of the mapping 00->0010, 01->010, 10->001, starting with 00.

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

Offset

1

Comments

The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289028.

Links

Clark Kimberling, Table of n, a(n) for n = 1..35312

Example

First six iterates of the mapping:
00
0010
0010001
001000100101
00100010010001010010
0010001001000101000100100100010001

Mathematica

z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "001"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289025 *)
Flatten[Position[st, 0]]  (* A289026 *)
Flatten[Position[st, 1]]  (* A289027 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289028 *)

Crossrefs

Cf. A289026, A289027, A289028.

Sequence in context: A221150 A288997 A276794 * A289112 A289165 A156729

Adjacent sequences: A289022 A289023 A289024 * A289026 A289027 A289028

Keyword

nonn,easy

Author

Clark Kimberling, Jun 27 2017

Status

approved