abstract
The Josephus problem
Lorenz Halbeisen and Norbert Hungerbühler
We give explicit non-recursive formulas to compute the
Josephus-numbers j(n,2,i) and j(n,3,i) and explicit upper and
lower bounds for j(n,k,i) (where k > 3) which differ by 2k-2
(for k=4 the bounds are even better). Furthermore we present a new
fast algorithm to calculate j(n,k,i) which is based upon the
mentioned bounds.