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%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
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