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Repdigits in Narayana's Cows Sequence and their Consequences
- Publication Year :
- 2020
-
Abstract
- 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.<br />Comment: Minor modifications, To appear in Journal of Integer Sequences
- Subjects :
- Mathematics - Number Theory
11B83, 11J86
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2007.12797
- Document Type :
- Working Paper