A289174 Fixed point of the mapping 00->0010, 01->100, 10->011, starting with 00.

0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 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 A289177.

Links

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

Example

The first six iterates of the mapping:
00
0010
0010011
00100111001
00100111001011100
0010011100101110010010110

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" -> "011"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289174 *)
Flatten[Position[st, 0]]  (* A289175 *)
Flatten[Position[st, 1]]  (* A289176 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289177 *)

Crossrefs

Cf. A289175, A289176, A289177.

Sequence in context: A288936 A064990 A284388 * A059125 A189820 A111406

Adjacent sequences: A289171 A289172 A289173 * A289175 A289176 A289177

Keyword

nonn,easy

Author

Clark Kimberling, Jun 29 2017

Status

approved