Power Fractional Parts

Author

Eric W. Weisstein
June 6, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/PowerFractionalParts.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PowerFractionalParts.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Graphics`Graphics`;
<<Statistics`DataManipulation`;

Fractional Part of ((((3/2)))^n)

NestList[3/2#&,1,10]

(f=FractionalPart[%])//InputForm

{Numerator[#],Denominator[#]}&@f

<<Graphics`FilledPlot`

FilledListPlot[FractionalPart[NestList[3/2#&,1,200]],PlotJoined->True,
AspectRatio->.4,AxesLabel->TraditionalForm/@{n,frac[(3/2)^n]}]

Distribution of fractional parts of power for constants

labels=Flatten[Table[{ToString[i]," "," "," "},{i,0,1,.2}]]

Block[
{$MaxExtraPrecision=Infinity},Show[GraphicsArray[Partition[BarChart[BinCounts[
N[Table[FractionalPart[#^n],{n,2000}],17],{0,1,.05}],
PlotRange->All,
BarSpacing->0,
BarLabels->labels,
DisplayFunction->Identity,
PlotLabel->TraditionalForm[#]]&/@{E,Pi,GoldenRatio,1+Sqrt[2]},2]]]
]//Timing