Geodesic
Jacobsthal-Lucas series and their applications
Algebra and discrete mathematics, Tome 24 (2017) no. 1, pp. 169-180

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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.
Keywords: Jacobsthal-Lucas sequence, the set of incomplete sums, singular random variable
Mots-clés : Hausdorff-Besicovitch dimension. 
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Mykola Pratsiovytyi; Dmitriy Karvatsky. Jacobsthal-Lucas series and their applications. Algebra and discrete mathematics, Tome 24 (2017) no. 1, pp. 169-180. http://geodesic.mathdoc.fr/item/ADM_2017_24_1_a10/