A288106 - OEIS

%I #5 Jun 07 2017 12:26:26

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

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

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

%N Fixed point of the mapping 00->0010, 1->00, starting with 00.

%H Clark Kimberling, <a href="/A288106/b288106.txt">Table of n, a(n) for n = 1..10000</a>

%e Iterates, starting with 00:

%e 00

%e 0010

%e 0010000

%e 00100000100010

%e 0010000010001000000100000

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

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

%t Table[w[n], {n, 0, 8}]

%t st = ToCharacterCode[w[11]] - 48   (* A288106 *)

%t Flatten[Position[st, 0]]  (* A287183 *)

%t Flatten[Position[st, 1]]  (* A287184 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A287185 conjectured *)

%Y Cf. A287183, A287184, A287185.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 06 2017