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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Computation of Jacobsthal’s function $h(n)$ for $n<50$.
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by Thomas R. Hagedorn PDF
Math. Comp. 78 (2009), 1073-1087

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 $n< 50$.
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Additional 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