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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Further tabulation of the Erdös-Selfridge function


Authors: Richard F. Lukes, Renate Scheidler and Hugh C. Williams
Journal: Math. Comp. 66 (1997), 1709-1717
MSC (1991): Primary 11N25, 11Y70, 11-04
MathSciNet review: 1422791
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Abstract: For a positive integer $k$, the Erdös-Selfridge function is the least integer $g(k) > k+1$ such that all prime factors of $\binom {g(k)}{k}$ exceed $k$. This paper describes a rapid method of tabulating $g(k)$ using VLSI based sieving hardware. We investigate the number of admissible residues for each modulus in the underlying sieving problem and relate this number to the size of $g(k)$. A table of values of $g(k)$ for $135 \leq k \leq 200$ is provided.


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Additional Information

Richard F. Lukes
Affiliation: Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Email: rflukes@cs.umanitoba.ca

Renate Scheidler
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Email: scheidle@math.udel.edu

Hugh C. Williams
Affiliation: Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Email: hugh_williams@csmail.cs.umanitoba.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00864-8
PII: S 0025-5718(97)00864-8
Received by editor(s): October 18, 1994
Received by editor(s) in revised form: October 9, 1995, and August 21, 1996
Additional Notes: The third author’s research is supported by NSERC of Canada grant A7649
Article copyright: © Copyright 1997 American Mathematical Society