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  Volume 4, Issue 2, Article 30
 
An Asymptotic Expansion
    Authors: Gabriel Mincu,  
    Keywords: Powers of primes, Inequalities, Asymptotic behaviour.  
    Date Received: 24/12/02  
    Date Accepted: 12/05/03  
    Subject Codes:

11N05,11N37

  
    Editors: László Tóth,  
 
    Abstract:

In this paper we study the asymptotic behaviour of the sequence $ % left(r_nright)_n$ of the powers of primes. Calculations also yield the evaluation $ sqrt{r_n}-p_n=oleft(frac{n}{mathnormal{log}^sn}right)$ for every positive integer s, $ p_n$ denoting the $ n$-th prime.

         
       
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