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The Josephus problem

Lorenz Halbeisen, Norbert Hungerbühler (1997)

Journal de théorie des nombres de Bordeaux

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 4 ) which differ by 2 k - 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.

The Markov-WZ method.

Mohammed, Mohamud, Zeilberger, Doron (2004)

The Electronic Journal of Combinatorics [electronic only]

Currently displaying 1781 – 1800 of 2016