A289128 Fixed point of the mapping 00->0010, 01->011, 10->010, starting with 00.

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

Offset

1

Comments

Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289131.

Links

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

Example

The first six iterates of the mapping:
00
0010
0010010
00100100110
001001001100101010
0010010011001010100110110110

Mathematica

z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "011", "10" -> "010"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289128 *)
Flatten[Position[st, 0]]  (* A289129 *)
Flatten[Position[st, 1]]  (* A289130 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289131 conjectured *)

Crossrefs

Cf. A289129, A289130, A289131.

Sequence in context: A340507 A072785 A188297 * A272664 A143518 A122414

Adjacent sequences: A289125 A289126 A289127 * A289129 A289130 A289131

Keyword

nonn,easy

Author

Clark Kimberling, Jun 28 2017

Status

approved