A289112 Fixed point of the mapping 00->0010, 01->011, 10->001, starting with 00.

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

Offset

1

Comments

Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289115.

Links

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

Example

The first six iterates of the mapping:
00
0010
0010001
001000100101
00100010010001011011
00100010010001011001001101100111

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" -> "001"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289112 *)
Flatten[Position[st, 0]]  (* A289113 *)
Flatten[Position[st, 1]]  (* A289114 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289115 conjectured *)

Crossrefs

Cf. A289112, A289113, A289114, A289115.

Sequence in context: A288997 A276794 A289025 * A289165 A156729 A188079

Adjacent sequences: A289109 A289110 A289111 * A289113 A289114 A289115

Keyword

nonn,easy

Author

Clark Kimberling, Jun 28 2017

Status

approved