Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers

Abstract

Let ${\left\{P_k\right\}}_{k\ge 0}$ 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 ${\left\{R_k\right\}}_{k\ge 0}$ 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 ${\left\{J_n\right\}}_{n\ge 0}$ 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.

The paper contains inaccuracies that need to be addressed before resubmission.