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arXiv · 2208.00276

Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers

Mustafa Ismail·Ahmed Gaber·M. Anwar
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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.

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Mustafa Ismail, Ahmed Gaber, M. Anwar. 2022-07-30. Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers. https://arxiv.org/abs/2208.00276

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