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Search: id:A087228
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| A087228 |
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a(n) is the smallest initial value at which initiating an iteration of Collatz-function and computing the LCM of arising terms, the number of distinct prime factors equals n. |
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+0
2
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| 2, 5, 3, 17, 11, 7, 9, 33, 67, 57, 59, 39, 105, 185, 191, 123, 225, 219, 239, 159, 319, 283, 251, 167, 335, 111, 297, 175, 233, 155, 103, 91, 107, 71, 31, 41, 27, 193, 129, 231, 171, 463, 327, 411, 859, 731, 487, 649, 639, 1153, 1563, 1607, 1071, 1215, 1307, 871, 1161
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n)=Min{x; A087227[x]=n}, where A087227(n)=A001221[A087226(n)], furthermore A087226(n)=LCM[terms trajectory started at n].
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EXAMPLE
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n=57: a(57)=10 because 57 is the smallest number such that
LCM of terms in its (3x+1)-trajectory,has 10 different
prime-factors: A082226(57)=864203580240=16.3.5.7.11.13.17.19.37.43.
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MATHEMATICA
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c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1)c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] ef[x_] := Length[FactorInteger[Apply[LCM, fpl[x]]]] t=Table[0, {256}]; Do[s=ef[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 1000}]; t
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CROSSREFS
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Cf. A006370, A087226, A086227, A078719, A001221.
Sequence in context: A002565 A063703 A109619 this_sequence A077216 A058357 A097754
Adjacent sequences: A087225 A087226 A087227 this_sequence A087229 A087230 A087231
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Aug 28 2003
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