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%I #9 Jul 18 2019 11:37:50
%S 1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,
%T 1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,1,1,1,
%U 0,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,1
%N Fixed point of the mapping 00->1000, 10->1001, starting at 00.
%C The first 5 iterates of the mapping:
%C 00
%C 1000
%C 10011000
%C 100010110011000
%C 100101001110010110011000
%C No iterate is an initial subword of its successor.
%H Clark Kimberling, <a href="/A288375/b288375.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" -> "1001"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[24]] - 48; (* A288375 *)
%t p0 = Flatten[Position[st, 0]]; (* A288625 *)
%t p1 = Flatten[Position[st, 1]]; (* A283794 *)
%t Table[StringLength[w[n]], {n, 0, 30}] (* A019274 *)
%Y Cf. A288625, A283794, A019274.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 24 2017
%E Definition corrected by _Georg Fischer_, Jul 18 2019
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