<abstract xmlns="http://www.w3.org/1999/xhtml">

Let <italic>p</italic><italic>n</italic> be the <italic>n</italic> th prime number. In this note, we study strictly increasing sequences of positive integers <italic>A</italic><italic>n</italic> such that the limit lim<italic>n</italic>→∞ (<italic>A</italic>1<italic>A</italic>2 <italic>· · · A</italic><italic>n</italic>)1<italic>/pn</italic> = <italic>e</italic> holds. This limit formula is in fact a generalization of some previously known results. Furthermore, some other generalizations are established.
</abstract>

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

General Limit Formulae Involving Prime Numbers

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"General Limit Formulae Involving Prime Numbers"}

Let pn be the n th prime number. In this note, we study strictly increasing sequences of positive integers An such that the limit limn→∞ (A1A2 · · · An)1/pn =...

General Limit Formulae Involving Prime Numbers

Published Online: Sep 08, 2022

Page range: 176 - 183

Received: Mar 28, 2022

Accepted: Aug 16, 2022

DOI: https://doi.org/10.2478/amsil-2022-0014

Keywords
limit formula, generalization, the number, prime numbers

© 2022 Reza Farhadian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

General Limit Formulae Involving Prime Numbers

Published Online: Sep 08, 2022

Page range: 176 - 183

Received: Mar 28, 2022

Accepted: Aug 16, 2022

DOI: https://doi.org/10.2478/amsil-2022-0014

Keywordslimit formula, generalization, the number, prime numbers

© 2022 Reza Farhadian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
limit formula, generalization, the number, prime numbers