A289165 - OEIS

%I #7 Apr 06 2020 22:05:12

%S 0,0,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0,

%T 1,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,

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

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

%C The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289168.

%H Clark Kimberling, <a href="/A289165/b289165.txt">Table of n, a(n) for n = 1..10000</a>

%e The first six iterates of the mapping:

%e 00

%e 0010

%e 0010001

%e 001000100101

%e 00100010010001100100

%e 0010001001000110000101000011000010

%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" -> "100", "10" -> "001"}]

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

%t st = ToCharacterCode[w[z]] - 48   (* A289165 *)

%t Flatten[Position[st, 0]]  (* A289166 *)

%t Flatten[Position[st, 1]]  (* A289167 *)

%t Table[StringLength[w[n]], {n, 0, 20}] (* A289168 *)

%Y Cf. A289166, A289167, A289168.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 29 2017