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Erdős-Turán Type Inequalities  
 
  Authors: Laurentiu Panaitopol,  
  Keywords: Powers of prime numbers, Inequalities, Erdős-Turán theorems.  
  Date Received: 10/01/03  
  Date Accepted: 19/02/03  
  Subject Codes:

11A25,11N05

  
  Editors: Jozsef Sandor,  
 
  Abstract:

Denoting by $(r_n)_{nge1}$ the increasing sequence of the numbers $p^alpha$ with $p$ prime and $alphage2$ integer, we prove that $r_{n+1}-2r_n+r_{n-1}$ is positive for infinitely many values of $n$ and negative also for infinitely many values of $n$. We prove similar properties for $%% r_n^2-r_{n-1}r_{n+1}$ and $frac{1}{r_{n-1}}-frac{2}{r_n}+frac{1}{r_{n+1}}$ as well.;


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