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

2023/12/29 by Mahadi Ddamulira, Ddamulira, Mahadi, Paul Emong +3 · 2 citations
Mathematics · #11B37 11D61 11J86 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.17571

openalex publication_date 2023/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (N_n)_{n≥ 0} be Narayana's cows sequence given by a recurrence relation N_n+3=N_n+2+N_n for all n≥ 0 , with initial conditions N₀=0 , and N₁= N₂=1 . In this paper, we find all members in Narayana's cow sequence that are palindromic concatenations of two distinct repdigits. Our proofs use techniques on Diophantine approximation which include the theory of linear forms in logarithms of algebraic numbers and Baker's reduction method. We show that 595 is the only member in Narayana's cow sequence that is a palindromic concatenation of two distinct repdigits in base 10.

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• Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits
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