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Mathematica Bohemica
Article . 2020
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https://doi.org/10.21136/mb.20...
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Lucas factoriangular numbers

english
descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 28 Nov 2018Publisher:Institute of Mathematics, Czech Academy of SciencesJournal:Mathematica Bohemica, volume 145, pages 33-43
Authors: Bir Kafle; Florian Luca; Alain Togbé;

doi: 10.21136/mb.2018.0021-18

Lucas factoriangular numbers

Abstract

A positive integer is a factoriangular number if it is of the form \(n!+n(n+1)/2\) for \(n\ge 0\), see [\textit{R. C. Castillo}, Asia Pac. J. Multidiscipl. Res. 3, No. 4, 5--11 (2015; \url{http://www.apjmr.com/wp-content/uploads/2015/10/APJMR-2015-3.4.1.02.pdf})]. \textit{C. A. Gómez Ruiz} and \textit{F. Luca} [Indag. Math., New Ser. 28, No. 4, 796--804 (2017; Zbl 1373.11011)] proved that the only Fibonacci factoriangular numbers (i.e., Fibonacci numbers which are factoriangular) are 2, 5 and 34. \textit{F. Luca} et al. [Publ. Inst. Math., Nouv. Sér. 105(119), 93--100 (2019; Zbl 1474.11092)] showed that the only Pell factoriangular numbers are 2, 5 and 12. The present authors show that the only Lucas factoriangular numbers are 1 and 2.

Keywords

lucas number, factoriangular number, QA1-939, Arithmetic functions; related numbers; inversion formulas, Lucas number, Fibonacci and Lucas numbers and polynomials and generalizations, Fibonacci type number, Lucas sequence, Mathematics, Linear forms in logarithms; Baker's method

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Published in a Diamond OA journal