General Limit Formulae Involving Prime Numbers

Reza Farhadian, Rafael Jakimczuk
2022 Annales Mathematicae Silesianae  
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 →∞ (A 1 A 2 · · · 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.
doi:10.2478/amsil-2022-0014 fatcat:wxg2enxbpzfwjbzie6k5hgvoce