On Palindromic forms in the k-Lucas sequence composed of two distinct Repdigits

2025/05/06 by Herbert Batte, Batte, Herbert, Prosper Kaggwa +1
Mathematics · Physics and Astronomy · #11B39 #11D45 #11D61 #11Y50 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #General Mathematics (math.GM) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.09638

openalex publication_date 2025/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For integers k ≥ 2, the k-generalized Lucas sequence \L_n^(k)\_{n ≥ 2-k} is defined by the recurrence relation L_n^(k) = L_n-1^(k) + ⋯ + L_n-k^(k) for n ≥ 2, with initial terms given by L₀^(k) = 2, L₁^(k) = 1, and L_2-k^(k) = ⋯ = L_-1^(k) = 0. In this paper, we extend work in \citeLucas and show that the result in \citeLucas still holds for k≥ 3, that is, we show that for k≥ 3, there is no k-generalized Lucas number appearing as a palindrome formed by concatenating two distinct repdigits.

Citations

• On k-Pell numbers that are Palindromes formed by two distinct Repdigits
• k-Fibonacci numbers that are palindromic concatenations of two distinct Repdigits
• Palindromic concatenations of two distinct repdigits in Narayana's cows sequence
• Lucas numbers that are palindromic concatenations of two distinct repdigits
• On the Largest Prime factor of the k-generalized Lucas numbers
• Classical and modular approaches to exponential Diophantine equations. I. Fibonacci and Lucas perfect powers

Related

• Lucas numbers that are palindromic concatenations of two distinct repdigits
• On k-Pell numbers that are Palindromes formed by two distinct Repdigits
• Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits
• On concatenations of two k-generalized Lucas numbers
• Almost Repdigits in k-generalized Lucas Sequences