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A285666
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Fixed point of the mapping 00->001, 1->010, starting with 00.
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3
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0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0
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OFFSET
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1
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COMMENTS
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Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A001580.
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LINKS
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EXAMPLE
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Iterates, starting with 00:
00
001
001010
00101000100
00101000100010010001
0010100010001001000100100010100010010
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MATHEMATICA
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s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "010"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A285666 *)
Flatten[Position[st, 0]] (* A285667 *)
Flatten[Position[st, 1]] (* A286058 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A001580 conjectured *)
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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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