Computation of Jacobsthal’s function $h(n)$ for $n<50$.
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- by Thomas R. Hagedorn;
- Math. Comp. 78 (2009), 1073-1087
- DOI: https://doi.org/10.1090/S0025-5718-08-02166-2
- Published electronically: November 20, 2008
Abstract:
Let $j(n)$ denote the smallest positive integer $m$ such that every sequence of $m$ consecutive integers contains an integer prime to $n$. Let $P_n$ be the product of the first $n$ primes and define $h(n)=j(P_n)$. Presently, $h(n)$ is only known for $n\leq 24$. In this paper, we describe an algorithm that enabled the calculation of $h(n)$ for $n< 50$.References
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Bibliographic Information
- Thomas R. Hagedorn
- Affiliation: Department of Mathematics and Statistics, The College of New Jersey. P.O. Box 7718, Ewing, New Jersey 08628-0718
- Email: hagedorn@tcnj.edu
- Received by editor(s): October 9, 2007
- Received by editor(s) in revised form: March 23, 2008
- Published electronically: November 20, 2008
- © Copyright 2009 by T. R. Hagedorn
- Journal: Math. Comp. 78 (2009), 1073-1087
- MSC (2000): Primary 11N25, 11Y55
- DOI: https://doi.org/10.1090/S0025-5718-08-02166-2
- MathSciNet review: 2476571