%I
%S 0,0,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0,0,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0,
%T 0,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0,0,0,1,1,0,0,0,0,1,0,1,0,1,
%U 0,0,0,0,1,0,0,0,1,1,0,0,1,0,0,1,0,0
%N Fixed point of the mapping 00>0001, 1>10, starting with 00.
%H Clark Kimberling, <a href="/A288377/b288377.txt">Table of n, a(n) for n = 1..10000</a>
%e Iterates, starting with 00:
%e 00
%e 0001
%e 0001010
%e 00010100100
%e 00010100100001100001
%e 00010100100001100001000110100001000110
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n  1], {"00" > "0001", "1" > "10"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[11]]  48 (* A288377 *)
%t Flatten[Position[st, 0]] (* A288378 *)
%t Flatten[Position[st, 1]] (* A288379 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A288380 conjectured *)
%Y Cf. A288378, A288379, A288380.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 09 2017
