论文标题
Padovan和Perrin数字作为两个Jacobsthal数字的总和
Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers
论文作者
论文摘要
令$ \ left \ lbrace p_ {k} \ right \ rbrace_ {k \ geq0} $是由$ p_ {k} = p_ {k-2}+p_ {k-3} $定义的padovan序列，其初始值是$ p_ {0} = p_ {0} = p_ {0} = p_ {k-3} $令$ \ left \ lbrace r_ {k} \ right \ rbrace_ {k \ geq0} $为perrin序列由$ r_ {k {k} = r_ {k-2}+r_ {k-2}+r_ {k-3} $，初始值为$ r_ {0} = 3 $ r_ = 3 $，$ r_} $ r_ {0} $ r_ {$ r_} $并让$ \ left \ lbrace j_ {n} \ right \ rbrace_ {n \ geq0} $为jacobsthal序列，由$ j_n = 2j_ {n-1}+j_ {n-2}+j_ {n-2} $ jacobsthal序列，带有缩写$ j_0 = 0 $ j_1 = 0 $，$ j_1 = 1 $。在本文中，我们确定了所有Padovan和Perrin编号，这些数字是两个Jacobsthal号码的总和。
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.
