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%I #10 May 28 2021 11:06:28
%S 1,0,0,1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,1,1,
%T 1,1,1,1,0,0,1,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,1,1,1,1,1,1,0,0,1,1,0,1,
%U 1,0,0,1,1,1,1,0,0,1,1,0,1,1,1,1,0,0
%N Fixed point of the mapping 00->1000, 10->10011, starting with 00.
%C Conjecture: The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A192967(n+2) for n >= 0.
%C Iterates, starting with 00:
%C 00
%C 1000
%C 100111000
%C 10011011100111000
%C 1001101100111110011011100111000
%C 100110110011110011011111001101100111110011011100111000
%C No iterate is an initial subword of its successor.
%H Clark Kimberling, <a href="/A288929/b288929.txt">Table of n, a(n) for n = 1..10000</a>
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "10011"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[11]] - 48 (* A288929 *)
%t Flatten[Position[st, 0]] (* A288930 *)
%t Flatten[Position[st, 1]] (* A288931 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A192967 conjectured *)
%Y Cf. A288930, A288931, A192967.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 25 2017
%E Definition corrected by _Georg Fischer_, May 28 2021
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