On a sequence involving the prime numbers

TL;DR

This paper investigates a prime number sequence by deriving asymptotic formulas and establishing improved bounds, advancing the understanding of prime-related sequences.

Contribution

It introduces new asymptotic formulas and tighter bounds for a prime number sequence, enhancing existing estimates.

Findings

Derived two asymptotic formulas for the sequence

Established new upper and lower bounds

Improved upon previous estimates

Abstract

In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.