A289165 Fixed point of the mapping 00->0010, 01->100, 10->001, starting with 00.

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

Offset

1

Comments

The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289168.

Links

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

Example

The first six iterates of the mapping:
00
0010
0010001
001000100101
00100010010001100100
0010001001000110000101000011000010

Mathematica

z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "001"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289165 *)
Flatten[Position[st, 0]]  (* A289166 *)
Flatten[Position[st, 1]]  (* A289167 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289168 *)

Crossrefs

Cf. A289166, A289167, A289168.

Sequence in context: A276794 A289025 A289112 * A156729 A188079 A049320

Adjacent sequences: A289162 A289163 A289164 * A289166 A289167 A289168

Keyword

nonn,easy

Author

Clark Kimberling, Jun 29 2017

Status

approved