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Prime factors of consecutive integers


Authors: Mark Bauer and Michael A. Bennett
Journal: Math. Comp. 77 (2008), 2455-2459
MSC (2000): Primary 11N25; Secondary 11D09
Published electronically: May 20, 2008
MathSciNet review: 2429894
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Abstract | References | Similar Articles | Additional Information

Abstract: This note contains a new algorithm for computing a function $ f(k)$ introduced by Erdős to measure the minimal gap size in the sequence of integers at least one of whose prime factors exceeds $ k$. This algorithm enables us to show that $ f(k)$ is not monotone, verifying a conjecture of Ecklund and Eggleton.


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Additional Information

Mark Bauer
Affiliation: Department of Mathematics, University of Calgary, Calgary AB
Email: mbauer@math.ucalgary.ca

Michael A. Bennett
Affiliation: Department of Mathematics, University of British Columbia, Vancouver BC
Email: bennett@math.ubc.ca

DOI: https://doi.org/10.1090/S0025-5718-08-02134-0
Received by editor(s): March 14, 2007
Published electronically: May 20, 2008
Additional Notes: The authors were supported in part by grants from NSERC
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.