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A289165
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Fixed point of the mapping 00->0010, 01->100, 10->001, starting with 00.
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6
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0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1
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OFFSET
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1
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COMMENTS
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The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289168.
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LINKS
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EXAMPLE
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The first six iterates of the mapping:
00
0010
0010001
001000100101
00100010010001100100
0010001001000110000101000011000010
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MATHEMATICA
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z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "001"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A289165 *)
Flatten[Position[st, 0]] (* A289166 *)
Flatten[Position[st, 1]] (* A289167 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289168 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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