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Mathematics of Computation

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Computation of Jacobsthal's function $ h(n)$ for $ n<50$.

Author: Thomas R. Hagedorn
Journal: Math. Comp. 78 (2009), 1073-1087
MSC (2000): Primary 11N25, 11Y55
Published electronically: November 20, 2008
MathSciNet review: 2476571
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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

Keywords: Jacobsthal function, killing sieve
Received by editor(s): October 9, 2007
Received by editor(s) in revised form: March 23, 2008
Published electronically: November 20, 2008
Article copyright: © Copyright 2009 by T. R. Hagedorn