General Limit Formulae Involving Prime Numbers

Reza Farhadian; Rafael Jakimczuk

doi:10.2478/amsil-2022-0014

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General Limit Formulae Involving Prime Numbers

Annales Mathematicae Silesianae

Volume 36 (2022): Issue 2 (September 2022)

By: Reza Farhadian and Rafael Jakimczuk

Open Access

|Sep 2022

Abstract

Let p_n be the n th prime number. In this note, we study strictly increasing sequences of positive integers A_n such that the limit lim_n_→∞ (A₁A₂ · · · A_n)¹^/pn = e holds. This limit formula is in fact a generalization of some previously known results. Furthermore, some other generalizations are established.

References

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2022-0014 | Journal eISSN: 2391-4238 (formerly 0860-2107) | Journal ISSN: 0860-2107

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Language: English

Page range: 176 - 183

Submitted on: Mar 28, 2022

Accepted on: Aug 16, 2022

Published on: Sep 8, 2022

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Keywords:

MSC:

11A41,

11A99,

40A20,

11Y60,

11B99

Related subjects:

Mathematics,

General mathematics

© 2022 Reza Farhadian, Rafael Jakimczuk, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 36 (2022): Issue 2 (September 2022)