A289011 Fixed point of the mapping 00->0010, 01->001, 10->100, starting with 00.

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

Offset

1

Comments

The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289010.

Links

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

Example

The first seven iterates of the mapping:
00
0010
0010100
00101001000
001010010000100100
0010100100001001000101000010010
0010100100001001000101000010010001001001000101000010

Mathematica

z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "100"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289011 *)
Flatten[Position[st, 0]]  (* A289012 *)
Flatten[Position[st, 1]]  (* A289013 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289000 *)

Crossrefs

Cf. A289008, A289009, A289000.

Sequence in context: A285666 A120325 A285139 * A289071 A287931 A372877

Adjacent sequences: A289008 A289009 A289010 * A289012 A289013 A289014

Keyword

nonn,easy

Author

Clark Kimberling, Jun 26 2017

Status

approved