On Generalized Lucas Pseudoprimality of Level k

Journal article

Andrica, Dorin and Bagdasar, Ovidiu 2021. On Generalized Lucas Pseudoprimality of Level k. Mathematics. 9 (8), p. 838. https://doi.org/10.3390/math9080838
AuthorsAndrica, Dorin and Bagdasar, Ovidiu
Abstract

We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k. We then use some recent arithmetic properties of the generalized Lucas, and generalized Pell–Lucas sequences, to define some new types of pseudoprimes of levels k+ and k− and parameter a. For these novel pseudoprime sequences we investigate some basic properties and calculate numerous associated integer sequences which we have added to the Online Encyclopedia of Integer Sequences.

KeywordsNumber theory; Numerical simulations
Year2021
JournalMathematics
Journal citation9 (8), p. 838
PublisherMDPI AG
ISSN2227-7390
Digital Object Identifier (DOI)https://doi.org/10.3390/math9080838
Web address (URL)http://hdl.handle.net/10545/625796
https://creativecommons.org/licenses/by/4.0/
hdl:10545/625796
Publication dates12 Apr 2021
Publication process dates
Deposited28 May 2021, 10:46
Accepted07 Apr 2021
ContributorsBabeş-Bolyai University, 400084 Cluj-Napoca, Romania and University of Derby
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Bagdasar, Ovidiu and Popa, Ioan-Lucian 2018. ENDM Proceedings for TREPAM'17: Preface. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.001
Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses.
Pratap, A., Raja, R., Sowmiya, C., Bagdasar, Ovidiu, Cao, Jinde and Rajchakit, Grienggrai 2018. Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. Neural Networks. https://doi.org/10.1016/j.neunet.2018.03.012
Unifying local-global type properties in vector optimization.
Bagdasar, Ovidiu and Popovici, Nicolae 2018. Unifying local-global type properties in vector optimization. Journal of Global Optimization. https://doi.org/10.1007/s10898-018-0656-8
Case studies: Using heuristics.
Lowndes, Val, Bagdasar, Ovidiu and Berry, Stuart 2017. Case studies: Using heuristics. in: Springer.
Further use of heuristic methods.
Lowndes, Val, Berry, Stuart, Parkes, Chris, Bagdasar, Ovidiu and Popovici, Nicolae 2017. Further use of heuristic methods. in: Springer.
On the geometry of certain periodic non-homogeneous Horadam sequences.
Bagdasar, Ovidiu and Popa, Ioan-Lucian 2016. On the geometry of certain periodic non-homogeneous Horadam sequences. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2016.11.002
New results and conjectures on 2-partitions of multisets.
Bagdasar, Ovidiu and Andrica, Dorin 2017. New results and conjectures on 2-partitions of multisets. Proceedings of the 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO). https://doi.org/10.1109/ICMSAO.2017.7934928
Qualitative case study methodology: Automatic design and correction of ceramic colors
Bagdasar, O., Birluţiu, A., Chen, M. and Popa, I.-L. 2017. Qualitative case study methodology: Automatic design and correction of ceramic colors. IEEE. https://doi.org/10.1109/icstcc.2017.8107118
New results and conjectures on 2-partitions of multisets
Bagdasar, O. and Andrica, D. 2017. New results and conjectures on 2-partitions of multisets. 7th International Conference on Modeling, Simulation, and Applied Optimization, ICMSAO 2017. IEEE Computer Society. https://doi.org/10.1109/icmsao.2017.7934928
ON THE MASKED PERIODICITY OF HORADAM SEQUENCES: A GENERATOR-BASED APPROACH
Bagdasar, Ovidiu D., Larcombe, Peter J. and Bagdasar, O. 2017. ON THE MASKED PERIODICITY OF HORADAM SEQUENCES: A GENERATOR-BASED APPROACH. Fibonacci Quarterly.
LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS
Bagdasar, Ovidiu, Popovici, Nicolae and Bagdasar, O. 2017. LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS. Journal of Nonlinear and Convex Analysis.
On the number of complex horadam sequences with a fixed period
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the number of complex horadam sequences with a fixed period. Fibonacci Quarterly.
On the characterization of periodic complex Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.
On a result of Bunder involving Horadam sequences: A proof and generalization
Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.
Influence discovery in semantic networks: An initial approach
Trovati, M. and Bagdasar, O. 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/uksim.2014.48
Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570
Concise computer mathematics: tutorials on theory and problems
Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.
On the characterization of periodic generalized Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022
Local 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/s11590-014-0781-3
A 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.2014.55
On 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-2019-0025
On 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
ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF
Larcombe, Peter J., Bagdasar, O. and Fennessey, Eric J. 2014. ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF. Fibonacci Quarterly. pp. 175-177.