Repdigits in Narayana's Cows Sequence and their Consequences

Members of Narayana's cow sequence that are concatenations of two repdigits

Let $ (N_n)_{n\ge 0}$ be the Narayana's cow sequence defined by a third-order recurrence relation $ N_0=0,\ N_1= N_2=1 $, and $ N_{n+3}=N_{n+2}+N_n $ for all $ n\ge 0 $. In this paper, we determine all Narayana numbers that are concatenations of two repdigits. The proof of our main theorem uses lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in Diophantine approximation.

Narayana奶牛序列中两个不同重位数的回文拼接

Palindromic concatenations of two distinct repdigits in Narayana's cows sequence

本文研究 Narayana 奶牛序列中两个不同重位数的回文拼接，利用丢番图逼近方法证明唯一成员为 595。

$k$-Fibonacci numbers which are Narayana's cows numbers

In this paper,we find all generalized Fibonacci numbers which are Narayana's cows numbers. In our proofs, we use both Baker's theory of nonzero linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction method.

关于Narayana数与重复数字数的两个问题

Two Problems on Narayana Numbers And Repeated Digit Numbers

本文研究Narayana数与重复数字数之间的乘积关系，完整刻画了可表示为Narayana数与重复数字数乘积的重复数字数，以及两个重复数字数乘积为Narayana数的情形。

基$\rho$下为三个重复数字串拼接的Narayana牛数

Narayana's cows numbers which are concatenations of three repdigits in base $ρ$

该数论研究针对Narayana序列，证明了基$\rho$下为三个重复数字串拼接的Narayana数的下标上界，并给出1≤ρ≤10时满足条件的最大数实例。

广义Pell序列与Narayana奶牛序列的公共项

Common terms of generalized Pell and Narayana's cows sequences

本文利用Matveev对数线性形式下界与连分数理论，完全求解了广义Pell序列与Narayana奶牛序列之间的丢番图方程，确定了二者全部公共项。