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A213672
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Final term in Collatz trajectory of n that did not appear in previous trajectories.
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1
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1, 2, 4, 0, 0, 6, 20, 0, 14, 0, 0, 12, 0, 0, 80, 0, 0, 18, 44, 0, 32, 0, 0, 24, 38, 0, 92, 0, 0, 30, 0, 0, 50, 0, 0, 36, 56, 0, 152, 0, 0, 42, 74, 0, 68, 0, 0, 48, 0, 0, 116, 0, 0, 54, 188, 0, 86, 0, 0, 60, 0, 0, 728, 0, 0, 66, 0, 0, 104, 0, 0, 72, 110, 0, 128, 0
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OFFSET
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1,2
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COMMENTS
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This can be considered as the step down value, as beyond this point the trajectory of n reduces to a lower trajectory. When n is impure we define a(n)=0; see also A177729.
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LINKS
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EXAMPLE
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a(7)=20 because after 20 trajectory of 7 becomes identical with trajectory of 3.
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MATHEMATICA
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Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; prev = {}; Table[c = Collatz[n]; If[Complement[c, prev] == {}, 0, i = 1; While[MemberQ[prev, c[[-i]]], i++]; prev = Union[prev, c]; c[[-i]]], {n, 100}] (* T. D. Noe, Mar 03 2013 *)
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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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