论文标题
Narayana的奶牛序列及其后果的重新划分
Repdigits in Narayana's Cows Sequence and their Consequences
论文作者
论文摘要
Narayana的奶牛序列满足第三阶线性复发关系$ n_n = n_ {n_ {n_ {n_ {n_ {n-3} $ for $ n \ geq 3 $ ting timital条件$ n_0 = 0 $ and $ n_0 = 0 $ and $ n_1 = n_1 = n_2 = n_2 = 1 $。在本文中，我们研究了$ b $ - 重新数字，这是两个Narayana数字的总和。我们明确确定基本$ 2 \ le B \ leq100 $作为插图的这些数字。我们还获得了有关Mersenne Prime数字，10个修复和具有不同数字块Narayana序列中数字的数字的结果。我们的主要定理的证明使用对数中线性形式的下限，以及在Diophantine近似中的Baker-Davenport减少方法的版本。
Narayana's cows sequence satisfies the third-order linear recurrence relation $N_n=N_{n-1}+N_{n-3}$ for $n \geq 3$ with initial conditions $N_0=0$ and $N_1=N_2=1$. In this paper, we study $b$-repdigits which are sums of two Narayana numbers. We explicitly determine these numbers for the bases $2\le b\leq100$ as an illustration. We also obtain results on the existence of Mersenne prime numbers, 10-repdigits, and numbers with distinct blocks of digits in the Narayana sequence. 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.
