A Study on the k-Mersenne and k-Mersenne-Lucas Sequences
In this study, we examine an application of $k-$Mersenne and $k-$Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas sequences have terms according to different v...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2025-03-01
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| Series: | Universal Journal of Mathematics and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4284061 |
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| author | Mine Uysal Hakan Akkuş Bayram Şen Engin Özkan |
| author_facet | Mine Uysal Hakan Akkuş Bayram Şen Engin Özkan |
| author_sort | Mine Uysal |
| collection | DOAJ |
| description | In this study, we examine an application of $k-$Mersenne and $k-$Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas sequences have terms according to different values of $k$, and some of them are associated with the sequences in OEIS. We obtain the generating functions of the Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas sequences. Moreover, we apply the Hankel transform to the Catalan transforms of these sequences. Finally, the determinants of the created matrices are calculated by applying the Hankel transform to the terms of the Catalan transforms of these sequences. |
| format | Article |
| id | doaj-art-e83afa90a3d74bbd83946ef57056a3df |
| institution | Kabale University |
| issn | 2619-9653 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj-art-e83afa90a3d74bbd83946ef57056a3df2025-08-20T03:53:38ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532025-03-01811710.32323/ujma.15662701225A Study on the k-Mersenne and k-Mersenne-Lucas SequencesMine Uysal0https://orcid.org/0000-0002-2362-3097Hakan Akkuş1https://orcid.org/0000-0001-9716-9424Bayram Şen2https://orcid.org/0009-0009-5570-4981Engin Özkan3https://orcid.org/0000-0002-4188-7248ERZINCAN BINALI YILDIRIM UNIVERSITYERZINCAN BINALI YILDIRIM UNIVERSITYERZINCAN BINALI YILDIRIM UNIVERSITYMarmara University, Faculty of SciencesIn this study, we examine an application of $k-$Mersenne and $k-$Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas sequences have terms according to different values of $k$, and some of them are associated with the sequences in OEIS. We obtain the generating functions of the Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas sequences. Moreover, we apply the Hankel transform to the Catalan transforms of these sequences. Finally, the determinants of the created matrices are calculated by applying the Hankel transform to the terms of the Catalan transforms of these sequences.https://dergipark.org.tr/en/download/article-file/4284061catalan numbersfibonacci numbersgenerating functionshankel transform$k$-mersenne sequences$k$-mersenne-lucas sequences |
| spellingShingle | Mine Uysal Hakan Akkuş Bayram Şen Engin Özkan A Study on the k-Mersenne and k-Mersenne-Lucas Sequences Universal Journal of Mathematics and Applications catalan numbers fibonacci numbers generating functions hankel transform $k$-mersenne sequences $k$-mersenne-lucas sequences |
| title | A Study on the k-Mersenne and k-Mersenne-Lucas Sequences |
| title_full | A Study on the k-Mersenne and k-Mersenne-Lucas Sequences |
| title_fullStr | A Study on the k-Mersenne and k-Mersenne-Lucas Sequences |
| title_full_unstemmed | A Study on the k-Mersenne and k-Mersenne-Lucas Sequences |
| title_short | A Study on the k-Mersenne and k-Mersenne-Lucas Sequences |
| title_sort | study on the k mersenne and k mersenne lucas sequences |
| topic | catalan numbers fibonacci numbers generating functions hankel transform $k$-mersenne sequences $k$-mersenne-lucas sequences |
| url | https://dergipark.org.tr/en/download/article-file/4284061 |
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