Prime factors of consecutive integers
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- by Mark Bauer and Michael A. Bennett PDF
- Math. Comp. 77 (2008), 2455-2459 Request permission
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.References
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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
- MR Author ID: 339361
- Email: bennett@math.ubc.ca
- Received by editor(s): March 14, 2007
- Published electronically: May 20, 2008
- Additional Notes: The authors were supported in part by grants from NSERC
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 2455-2459
- MSC (2000): Primary 11N25; Secondary 11D09
- DOI: https://doi.org/10.1090/S0025-5718-08-02134-0
- MathSciNet review: 2429894