%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