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On the Sequence $(p_n^2-p_{n-1}p_{n+1})_{n\ge 2}$  
 
  Authors: Laurentiu Panaitopol,  
  Keywords: Prime Numbers, Sequences, Series, Asymptotic Behaviour.  
  Date Received: 17/12/01  
  Date Accepted: 24/05/02  
  Subject Codes:

11A25,11N05,

  
  Editors: László Tóth,  
 
  Abstract:

Let $ p_n$ be the $ n$-th prime number and $ x_n=p_n^2-p_{n-1}p_{n+1}$. In this paper, we study sequences containing the terms of the sequence $ (x_n)_{nge 1}$. The main result asserts that the series $ sum_{n=1}^{infty}x_n/p_n^2$ is convergent, without being absolutely convergent.;


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