Demlo Number

Author

Eric W. Weisstein
February 17, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Initialization

Repunit[n_]:=(10^n-1)/9
Demlo[n_]:=Repunit[n]^2
SetAttributes[Demlo,Listable]

Enumeration

Demlo[Range[11]]

Generating Function

Series[-((10*x+1)/((x-1)*(10*x-1)*(100*x-1))),{x,0,11}]

SeriesCoefficient[-((10x+1)/((x-1)(10x-1)(100x-1))),{x,0,n}]

Table[(1/81) (((-1+(10^(1+n))))^2),{n,0,10}]

Sum of Digits

Simplify[Sum[k+(k-1),{k,n}]]

digsum=(Plus@@IntegerDigits[#])&/@Demlo[Range[100]]

Timing[p=Position[digsum=Sqrt[(Plus@@IntegerDigits[#])&/@Demlo[Range[2500]]],_Integer,{1}]//Flatten]

Sums of Squares of Digits

digsum2=(Plus@@(IntegerDigits[#]^2))&/@Demlo[Range[60]]