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%I #7 Apr 07 2020 21:27:49
%S 0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,1,0,1,
%T 0,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,
%U 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0
%N Fixed point of the mapping 00->0010, 01->011, 10->010, 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 A289131.
%H Clark Kimberling, <a href="/A289128/b289128.txt">Table of n, a(n) for n = 1..10000</a>
%e The first six iterates of the mapping:
%e 00
%e 0010
%e 0010010
%e 00100100110
%e 001001001100101010
%e 0010010011001010100110110110
%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" -> "011", "10" -> "010"}]
%t TableForm[Table[w[n], {n, 0, 10}]]
%t st = ToCharacterCode[w[z]] - 48 (* A289128 *)
%t Flatten[Position[st, 0]] (* A289129 *)
%t Flatten[Position[st, 1]] (* A289130 *)
%t Table[StringLength[w[n]], {n, 0, 20}] (* A289131 conjectured *)
%Y Cf. A289129, A289130, A289131.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 28 2017
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