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A288858
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2-limiting word of the mapping 00->1000, 10->011, starting with 00.
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7
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0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1
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OFFSET
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1
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COMMENTS
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Iterates of the mapping, starting with 00:
00
1000
0111000
0110111000
01011110111000
0011111011110111000
10001111011111011110111000
01110001110111111011111011110111000
011011100011011111110111111011111011110111000
The 2-limiting word is the limit of the n-th iterates for n == 2 mod 5.
The number of letters (0's and 1's) in the n-th iterate is given by A288243(n), for n >= 0.
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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 two n-th iterates for n == 2 mod 5: 0111000 and 01110001110111111011111011110111000. (The lengths of the first 10 such iterates are 7, 35, 106, 242, 473, 849, 1442, 2346, 3685, 5642.)
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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" -> "1000", "10" -> "011"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[52]] - 48 (* A288858 *)
Flatten[Position[st, 0]] (* A288859 *)
Flatten[Position[st, 1]] (* A288860 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)
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CROSSREFS
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Cf. A288226 (0-limiting word), A288855 (1-limiting word), A288861 (3-limiting word), A288864 (4-limiting word), A288859, A288860, A288243.
Sequence in context: A029693 A200263 A051067 * A356313 A309218 A189718
Adjacent sequences: A288855 A288856 A288857 * A288859 A288860 A288861
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Jun 23 2017
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STATUS
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approved
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