A289016 Fixed point of the mapping 00->0010, 01->010, 10->000, starting with 00.

0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 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, 0, 0, 0, 1, 0, 0, 0, 0, 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 A289019.

Links

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

Example

The first six iterates of the mapping:
00
0010
0010000
001000000100
0010000001000100100010
001000000100010010001001000100000010000

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" -> "000"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289016 *)
Flatten[Position[st, 0]]  (* A289017 *)
Flatten[Position[st, 1]]  (* A289018 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289019 *)

Crossrefs

Cf. A289017, A289018, A289019.

Sequence in context: A025455 A288167 A288991 * A289104 A289235 A188371

Adjacent sequences: A289013 A289014 A289015 * A289017 A289018 A289019

Keyword

nonn,easy

Author

Clark Kimberling, Jun 26 2017

Status

approved