Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm135-1-5,
author = {Jean-Marie De Koninck and Imre K\'atai},
title = {Normal numbers and the middle prime factor of an integer},
journal = {Colloquium Mathematicae},
volume = {135},
year = {2014},
pages = {69-77},
zbl = {1304.11071},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm135-1-5}
}
Jean-Marie De Koninck; Imre Kátai. Normal numbers and the middle prime factor of an integer. Colloquium Mathematicae, Tome 135 (2014) pp. 69-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm135-1-5/