%I #7 Apr 06 2020 20:10:02

%S 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,

%T 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,

%U 0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0

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

%C The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289019.

%H Clark Kimberling, <a href="/A289016/b289016.txt">Table of n, a(n) for n = 1..10000</a>

%e The first six iterates of the mapping:

%e 00

%e 0010

%e 0010000

%e 001000000100

%e 0010000001000100100010

%e 001000000100010010001001000100000010000

%t z = 11; (* number of iterates *)

%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "000"}]

%t TableForm[Table[w[n], {n, 0, 10}]]

%t st = ToCharacterCode[w[z]] - 48 (* A289016 *)

%t Flatten[Position[st, 0]] (* A289017 *)

%t Flatten[Position[st, 1]] (* A289018 *)

%t Table[StringLength[w[n]], {n, 0, 20}] (* A289019 *)

%Y Cf. A289017, A289018, A289019.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 26 2017