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Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers
- Publication Year :
- 2022
-
Abstract
- 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.<br />Comment: The paper contains inaccuracies that need to be addressed before resubmission.
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.00276
- Document Type :
- Working Paper