Remote Access Mathematics of Computation
Green Open Access

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
DOI: https://doi.org/10.1090/S0025-5718-97-00864-8
MathSciNet review: 1422791
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. R. Scheidler and H. C. Williams, A method of tabulating the number theoretic function $g(k)$, Math. Comp. 59 (1992), 251-257. MR 92k:11146
  • 2. E. F. Ecklund, P. Erdös and J. L. Selfridge, A new function associated with the prime factors of $(^{n}_{k})$, Math. Comp. 28 (1974), 647-649. MR 49:2501
  • 3. P. Erdös, C. B. Lacampagne and J. L. Selfridge, Estimates of the least prime factor of a binomial coefficient, Math. Comp. 61 (1993), 215-224. MR 93k:11013
  • 4. R. F. Lukes, C. D. Patterson and H. C. Williams, Numerical Sieving Devices: Their History and Some Applications, Nieuw Archiv voor Wiskunde 13, ser. 4, no. 1 (1995), 113-139. MR 96m:11082
  • 5. A. Granville and O. Ramaré, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika, 43 (1996), 73-107. CMP 96:16
  • 6. L. E. Dickson, History of the Theory of Numbers, vol. 1, Chelsea, New York, 1966. MR 39:6807a

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (1991): 11N25, 11Y70, 11-04

Retrieve articles in all journals with MSC (1991): 11N25, 11Y70, 11-04


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: https://doi.org/10.1090/S0025-5718-97-00864-8
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

American Mathematical Society