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  Volume 3, Issue 4, Article 53
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:


    Editors: László Tóth,  

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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