%I #4 Jun 04 2017 18:18:21
%S 0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,
%T 0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,
%U 1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0
%N Fixed point of the mapping 00->001, 1->000, starting with 00.
%H Clark Kimberling, <a href="/A286939/b286939.txt">Table of n, a(n) for n = 1..10000</a>
%e Iterates, starting with 00:
%e 00
%e 001
%e 001000
%e 0010000010
%e 00100000100100000
%e 00100000100100000010000010010
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "000"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[11]] - 48 (* A286939 *)
%t Flatten[Position[st, 0]] (* A285432 *)
%t Flatten[Position[st, 1]] (* A285564 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A285665 conjectured *)
%Y Cf. A285432, A285564, A285665.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 04 2017