An upper bound on Jacobsthal’s function
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- by Fintan Costello and Paul Watts;
- Math. Comp. 84 (2015), 1389-1399
- DOI: https://doi.org/10.1090/S0025-5718-2014-02896-2
- Published electronically: November 6, 2014
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Abstract:
The function $h(k)$ represents the smallest number $m$ such that every sequence of $m$ consecutive integers contains an integer coprime to the first $k$ primes. We give a new computational method for calculating strong upper bounds on $h(k)$.References
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Bibliographic Information
- Fintan Costello
- Affiliation: School of Computer Science and Informatics, University College Dublin, Belfield, Dublin 6, Ireland
- Email: fintan.costello@ucd.ie
- Paul Watts
- Affiliation: Department of Mathematical Physics, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland
- Email: watts@thphys.nuim.ie
- Received by editor(s): May 24, 2012
- Received by editor(s) in revised form: September 16, 2013, and September 26, 2013
- Published electronically: November 6, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 1389-1399
- MSC (2010): Primary 11N25; Secondary 11Y55
- DOI: https://doi.org/10.1090/S0025-5718-2014-02896-2
- MathSciNet review: 3315513