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Mathematics of Computation

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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: 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

Michael A. Bennett
Affiliation: Department of Mathematics, University of British Columbia, Vancouver BC

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.

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