On some new results for the generalised Lucas sequences
Journal article
Andrica, D., Bagdasar, O. and Turcaş, G.C. 2021. On some new results for the generalised Lucas sequences. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. Volume 29 (Issue 1), pp. 17 - 36. https://doi.org/10.2478/auom-2021-0002
| Authors | Andrica, D., Bagdasar, O. and Turcaş, G.C. |
|---|---|
| Abstract | In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits for them (Theorem 6). We formulate necessary and sufficient arithmetic conditions which can identify the terms of a-Fibonacci and a-Lucas sequences. Finally, using a deep theorem of Siegel, we show that the aforementioned sequences contain only finitely many perfect powers. During the process we also discover some novel integer sequences. |
| Keywords | Generalised Lucas sequence; Generalised Pell-Lucas sequence; Negative Pell equation; Pell equation; Special Pell Equation |
| Year | 2021 |
| Journal | Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica |
| Journal citation | Volume 29 (Issue 1), pp. 17 - 36 |
| Publisher | Sciendo |
| ISSN | 1844-0835 |
| 12241784 | |
| Digital Object Identifier (DOI) | https://doi.org/10.2478/auom-2021-0002 |
| Web address (URL) | http://www.scopus.com/inward/record.url?eid=2-s2.0-85103261361&partnerID=MN8TOARS |
| https://sciendo.com/article/10.2478/auom-2021-0002 | |
| Output status | Published |
| Publication dates | Mar 2021 |
| Online | 13 Apr 2021 |
| Publication process dates | |
| Accepted | 25 May 2020 |
| Deposited | 25 May 2023 |
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Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022Local maximum points of explicitly quasiconvex functions
Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3A horadam-based pseudo-random number generator
Bagdasar, O.D., Chen, M. and Bagdasar, O. 2014. A horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/uksim.2014.55On the structure of periodic complex Horadam orbits
Bagdasar, Ovidiu D., Larcombe, Peter J., Anjum, Ashiq and Bagdasar, O. 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics.Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems
Popa, I.-L., Ceauşu, T., Bagdasar, O. and Agarwal, R.P. 2016. Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 27 (2), pp. 153-166. https://doi.org/10.2478/auom-2019-0025On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B