A289074 Fixed point of the mapping 00->0010, 01->011, 10->100, starting with 00.

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

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 six iterates of the mapping:
00
0010
0010100
00101001000
001010010001000100
0010100100010001001000100100010

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" -> "100"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289074 *)
Flatten[Position[st, 0]]  (* A289075 *)
Flatten[Position[st, 1]]  (* A289076 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289077 *)

Crossrefs

Cf. A289075, A289076, A289077.

Sequence in context: A289011 A289071 A287931 * A289242 A346218 A188037

Adjacent sequences: A289071 A289072 A289073 * A289075 A289076 A289077

Keyword

nonn,easy

Author

Clark Kimberling, Jun 27 2017

Status

approved