The Josephus Problem
نویسنده
چکیده
Lorenz Halbeisen, ETH Z urich Norbert Hungerb uhler, University of Freiburg (Germany) Abstract 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 di er 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.
منابع مشابه
A Comparative Study on the Algorithms for a Generalized Josephus Problem
The classic Josephus problem can be described as follows: There are n objects, consecutively numbered from 1 through n, arranged in a circle. We are given a positive integer k. Beginning with a designated first object, we proceed around the circle, removing every kth object. After each object is removed, counting continues around the circle that remains. This process continues until all n objec...
متن کاملJosephus' Portrait of Asa
Whereas the rabbinic tradition attacks King Asa of Judah for trusting in himself rather than in G-d and, in particular, for drafting the sages, Josephus, the apologist, omits such details and, indeed, whitewashes Asa completely. He is praised particularly, in language reminiscent of Josephus' portraits of Saul and David, as well as of Thucydides' Pericles, for putting his nation in order. In pa...
متن کاملJosephus' Portrait of Jeroboam
A number of studies have been published of Josephus' portraits of biblical heroes, wherein we see that Josephus systematically aggrandizes their qualities of good birth, handsomeness, and the cardinal virtues of wisdom, courage, temperance, justice, and piety? But how does he depict biblical rogues? Three Israelite kings whose wickedness is emphasized in the biblical record-namely, Jeroboam I, ...
متن کاملistributed Interactive Simulation of Combat INTRODUCTION: PREPARING FOR THE NEXT WAR
[The Romans] do not begin to use their weapons first in time of war, nor do they then put their hands first into motion, while they avoided so to do in times of peace; but as if their weapons did always cling to them, they have never any truce from warlike exercises; . . . nor would he be mistaken that should call those their exercises unbloody battles, and their battles bloody exercises.— Flav...
متن کاملPermuting operations on strings and their relation to prime numbers
Some length-preserving operations on strings only permute the symbol positions in strings; such an operation X gives rise to a family {Xn}n≥2 of similar permutations. We investigate the structure and the order of the cyclic group generated by Xn. We call an integer n X-prime if Xn consists of a single cycle of length n (n ≥ 2). Then we show some properties of these X-primes, particularly, how X...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997