Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866917779970457600 |
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| author | Ismail, Mustafa Gaber, Ahmed Anwar, M. |
| author_facet | Ismail, Mustafa Gaber, Ahmed Anwar, M. |
| contents | Let $\left\lbrace P_{k}\right\rbrace_{k\geq0}$ be the Padovan sequence defined by $P_{k}=P_{k-2}+P_{k-3}$ with initial values are $P_{0}=P_{1}=P_{2}=1$. Let $\left\lbrace R_{k}\right\rbrace_{k\geq0}$ be the Perrin sequence defined by $R_{k}=R_{k-2}+R_{k-3}$ with initial values are $R_{0}=3$, $R_{1}=0$, $R_{2}=2$. And let $\left\lbrace J_{n}\right\rbrace_{n\geq0}$ be the Jacobsthal sequence defined by $J_n=2J_{n-1}+J_{n-2}$ with initials $J_0=0$, $J_1=1$. In this paper we determine all Padovan and Perrin numbers which are sum of two Jacobsthal number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00276 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers Ismail, Mustafa Gaber, Ahmed Anwar, M. Number Theory Let $\left\lbrace P_{k}\right\rbrace_{k\geq0}$ be the Padovan sequence defined by $P_{k}=P_{k-2}+P_{k-3}$ with initial values are $P_{0}=P_{1}=P_{2}=1$. Let $\left\lbrace R_{k}\right\rbrace_{k\geq0}$ be the Perrin sequence defined by $R_{k}=R_{k-2}+R_{k-3}$ with initial values are $R_{0}=3$, $R_{1}=0$, $R_{2}=2$. And let $\left\lbrace J_{n}\right\rbrace_{n\geq0}$ be the Jacobsthal sequence defined by $J_n=2J_{n-1}+J_{n-2}$ with initials $J_0=0$, $J_1=1$. In this paper we determine all Padovan and Perrin numbers which are sum of two Jacobsthal number. |
| title | Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2208.00276 |