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Consequences of a Theorem of Erdös-Prachar  
 
  Authors: Laurentiu Panaitopol,  
  Keywords: Sequences, Series, Prime Numbers, the Sequence of Composed Numbers, Asymptotic Formula  
  Date Received: 27/03/01  
  Date Accepted: 11/06/01  
  Subject Codes:

11A25,11N05

  
  Editors: László Tóth,  
 
  Abstract:

We study the asymptotic behavior of the sums $ sumlimits_{nle x}leftvertfrac{c_{n+1}}{p_{n+1}}-frac{c_n}{p_n}rightvert$ and $ sumlimits_{nle x}leftvertfrac{p_{n+1}}{c_{n+1}}-frac{p_n}{c_n rightvert$, and of the series $ sumlimits_{n=1}^{infty} leftvertfrac{c_{n+1}}{p_{n+1}}-frac{c_n}{p_n}rightvert^{alpha}$, where $ p_n$ denotes the $ n$-th prime number while $ c_n$ stands for the $ n$-th composed number.;


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