On the Sequence $(p_n^2-p_{n-1}p_{n+1})

Volume 3, Issue 4, 2002

Article 53

ON THE SEQUENCE $(p_n^2-p_{n-1}p_{n+1})_{n\ge 2}$

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

Received 17 December, 2001; Accepted 24 May, 2002.
Communicated by: L. Toth

ABSTRACT. Let

be the

-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 $(x_n)_{n\ge 1}$ . The main result asserts that the series $\sum_{n=1}^{\infty}x_n/p_n^2$ is convergent, without being absolutely convergent.

Key words:
Prime Numbers, Sequences, Series, Asymptotic Behaviour.

2000 Mathematics Subject Classification:
11A25, 11N05, 11N36.

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