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%I #10 Apr 06 2020 22:11:06
%S 0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,0,1,0,
%T 0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,1,0,0,
%U 1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0
%N Fixed point of the mapping 00->0010, 01->100, 10->100, 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 A289004.
%H Clark Kimberling, <a href="/A289242/b289242.txt">Table of n, a(n) for n = 1..10000</a>
%e The first six iterates of the mapping:
%e 00
%e 0010
%e 0010100
%e 00101001000
%e 001010010010000100
%e 0010100100100001010000101000010
%t z = 11; (* number of iterates *)
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "100"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289242 *)
%t Flatten[Position[st, 0]] (* A289243 *)
%t Flatten[Position[st, 1]] (* A289244 *)
%t Table[StringLength[w[n]], {n, 0, 20}] (* A289004 *)
%Y Cf. A289243, A289244, A289004.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jul 01 2017
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