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Normal numbers and the middle prime factor of an integer

Volume 135 / 2014

Jean-Marie De Koninck, Imre Kátai Colloquium Mathematicum 135 (2014), 69-77 MSC: Primary 11K16; Secondary 11N37. DOI: 10.4064/cm135-1-5

Abstract

Let $p_m(n)$ stand for the middle prime factor of the integer $n\ge 2$. We first establish that the size of $\log p_m(n)$ is close to $\sqrt {\log n}$ for almost all $n$. We then show how one can use the successive values of $p_m(n)$ to generate a normal number in any given base $D\ge 2$. Finally, we study the behavior of exponential sums involving the middle prime factor function.

Authors

  • Jean-Marie De KoninckDépartement de mathématiques et de statistique
    Université Laval
    Québec, QC G1V 0A6, Canada
    e-mail
  • Imre KátaiComputer Algebra Department
    Eötvös Lorand University
    Pázmány Péter sétány 1/C
    1117 Budapest, Hungary
    e-mail

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