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%I #9 Apr 07 2020 21:48:07
%S 0,0,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,0,1,0,0,0,1,0,1,0,0,1,0,0,1,
%T 0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,
%U 0,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0,0
%N Fixed point of the mapping 00->001, 1->10, starting with 00.
%C The number of letters (0's and 1's) in the n-th iterate, beginning with 2,3,5,8,13, is given by A286938, which appears to be the same as A164457 except for initial 2,3,5.
%H Clark Kimberling, <a href="/A284932/b284932.txt">Table of n, a(n) for n = 1..10000</a>
%e Iterates, starting with 00:
%e 00
%e 001
%e 00110
%e 00110100
%e 0011010010001
%e 001101001000110001010
%e 001101001000110001010100010100100
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "10"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[11]] - 48 (* A284932 *)
%t Flatten[Position[st, 0]] (* A285352 *)
%t Flatten[Position[st, 1]] (* A285303 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A286938 *)
%Y Cf. A285352, A285303, A286938, A164457.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 03 2017
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