Binary Champernowne Constant

Author

Eric W. Weisstein
June 30, 2013

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/BinaryChampernowneConstant.nb.

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

©2013 Wolfram Research, Inc. except for portions noted otherwise

Value

N[ChampernowneNumber[2],1000]

ChampernowneN[2,10]

BaseForm[ChampernowneN[2,10],2]

RealDigits[ChampernowneN[2,20],2]

ChampernowneN[2,100]

RealDigits[ChampernowneN[2,100]]

ContinuedFraction[Champernowne[1000]]

IntegerLength/@ContinuedFraction[N[ChampernowneNumber[2],1000]]

F[n_]:=n+Sum[Floor[Log[2,k]],{k,n}]

F[n]

Table[F[n],{n,20}]

Sum[n/2^F[n],{n,∞}]

NSum[n/2^F[n],{n,∞}]

2.^F[100]

N[Sum[n/2^F[n],{n,100}],100]//Timing

2.^F[1000]

N[Sum[n/2^F[n],{n,1000}],100]//Timing