Erdos-Turan Type Inequalities

Volume 4, Issue 1, 2003

Article 23

ERDÕS-TURÁN TYPE INEQUALITIES

UNIVERSITY OF BUCHAREST
FACULTY OF MATHEMATICS
14 ACADEMIEI ST.
RO--70109 BUCHAREST
ROMANIA.
E-Mail: pan@al.math.unibuc.ro

Received 10 January, 2003; Accepted 19 February, 2003.
Communicated by: J. Sandor

ABSTRACT. Denoting by $(r_n)_{n\ge1}$ the increasing sequence of the numbers $p^\alpha$ with

prime and $\alpha\ge2$ integer, we prove that $r_{n+1}-2r_n+r_{n-1}$ is positive for infinitely many values of

and negative also for infinitely many values of

. 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.

Key words:
Powers of prime numbers, Inequalities, Erdõs-Turán theorems.

2000 Mathematics Subject Classification:
11A25, 11N05.

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