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A180864
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Trajectory of 13 under map n->A006368(n).
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18
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13, 10, 15, 11, 8, 12, 18, 27, 20, 30, 45, 34, 51, 38, 57, 43, 32, 48, 72, 108, 162, 243, 182, 273, 205, 154, 231, 173, 130, 195, 146, 219, 164, 246, 369, 277, 208, 312, 468, 702, 1053, 790, 1185, 889, 667, 500, 750, 1125, 844, 1266, 1899, 1424, 2136, 3204, 4806, 7209, 5407, 4055, 3041, 2281, 1711, 1283, 962
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Merges with the trajectory of 8 after four steps - see A028393.
It is a famous unsolved problem to show that this trajectory is unbounded.
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REFERENCES
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D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998; see p. 16.
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LINKS
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FORMULA
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MATHEMATICA
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b[n_] := If[EvenQ[n], 3n/2, Floor[(3n+2)/4]];
a[0] = 13; a[n_] := a[n] = b[a[n-1]];
SubstitutionSystem[{n_ :> If[EvenQ[n], 3n/2, Round[3n/4]]}, {13}, 62] // Flatten (* Jean-François Alcover, Mar 01 2019 *)
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PROG
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(Haskell)
a180864 n = a180864_list !! n
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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