Jacobsthal-Lucas series and their applications

Mykola Pratsiovytyi, Dmitriy Karvatsky


In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence (\(J_{n+2}=2J_{n+1}+J_n\), \(J_1=2\), \(J_2=1\)). In particular, we consider the properties of the set of incomplete sums as well as their applications. We prove that the set of incomplete sums of this series is a nowhere dense set of positive Lebesgue measure. Also we study singular random variables of Cantor type related to Jacobsthal-Lucas sequence.


Jacobsthal-Lucas sequence, set of incomplete sums, singular random variable, Hausdorff-Besicovitch dimension

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