APPENDIX

It is easier to study this variant of the Josephus Problem using computer programs.

If you want to use the computer algebra system Mathematica, please visit the following homepage.
http://demonstrations.wolfram.com/TheLinearJosephusProblem/
By downloading a Mathematica Player for free you can use this Mathematica program. In this Mathematica program $n$ can be $1,2, ...,21$, and $1\leq k \leq n$.
If you have Mathematica 6, then you will find our Mathematica notebook useful for studying this variant of the Josephus Problem. The authors have uploaded our Mathematica file "NewJosephus.nb" at the following address.
http://library.wolfram.com/infocenter/MathSource/7164
With this Mathematica 6.0 file you can study the problem further.

Acknowledgments
The authors have used the computer algebra system Mathematica throughout our research. As to the research by Mathematica see [1],[3] and [6].