Volume 2,  Issue 3, 2001

Article 38

SOME PROPERTIES OF THE SERIES OF COMPOSED NUMBERS

LAURENTIU PANAITOPOL

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

Received 27 March, 2001; accepted 11 June, 2001.
Communicated by: L. Toth


ABSTRACT.    $ c_n$ denotes the $ n$-th composed number, one proves inequalities involving $ c_n, p_{c_n}, c_{p_n}$, and shows that the sequences $ (p_n)_{n\ge 1}$ and $ (c_{p_n})_{n\ge 1}$ are neither convex nor concave.
Key words:
Prime Numbers, Composed Numbers, Asymptotic Behavior, Inequalities, Sums and Series.

2000 Mathematics Subject Classification:
11A25, 11N05.


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On Some Generalizations of Steffensen's Inequality and Related Results
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Good Lower and Upper Bounds on Binomial Coefficients
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Improvement of an Ostrowski Type Inequality for Monotonic Mappings and its Application for Some Special Means
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On the Utility of the Telyakovskii's Class S
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L'Hospital Type Rules for Oscillation, with Applications
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Matrix and Operator Inequalities
Fozi M. Dannan

Consequences of a Theorem of Erdös-Prachar
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On a Reverse of Jessen's Inequality for Isotonic Linear Functionals
S.S. Dragomir 

Lp-Improving Properties for Measures on R4 Supported on Homogeneous Surfaces in Some Non Elliptic Cases
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Some Properties of the Series of Composed Numbers
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