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A288512
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1-limiting word of the mapping 00->0101, 10->001, starting with 00.
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3
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0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 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 is given by A288511(n).
Iterates, starting with 00:
00
0101
00011
0101011
000100111
010100010111
00010010101001111
01010001000100100101111
000100101010010101001000100011111
The 1-limiting word is the limit taken over odd-numbered iterations of the mapping.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..10000
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EXAMPLE
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The first 4 odd-numberd iterates:
0101
0101011
010100010111
01010001000100100101111
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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" -> "0101", "10" -> "001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[19]] - 48 (* A288512 *)
Flatten[Position[st, 0]] (* A288513 *)
Flatten[Position[st, 1]] (* A288514 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288511 conjectured *)
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CROSSREFS
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Cf. A288511, A288513, A288514.
Sequence in context: A353811 A116865 A353674 * A157687 A189668 A353525
Adjacent sequences: A288509 A288510 A288511 * A288513 A288514 A288515
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Jun 12 2017
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STATUS
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approved
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