4 papers
math.NT2026
On mixed -concatenations of Fibonacci and Lucas numbers that are Lucas numbers
Herbert Batte, Prosper Kaggwa
Let and denote the sequences of Fibonacci and Lucas numbers respectively. This paper determines all Lucas numbers that can be represented as base $b…
math.NT2025
On concatenations of two -generalized Lucas numbers
Alex Behakanira Tumwesigye, Mahadi Ddamulira, Prosper Kaggwa
For an integer \( k \geq 2 \), the sequence of \( k \)-generalized Lucas numbers is defined by the recurrence relation \( L_n^{(k)} = L_{n-1}^{(k)} + \cdots + L_{n-k}^{(k)} \) for…
math.GM2025
On Palindromic forms in the -Lucas sequence composed of two distinct Repdigits
Herbert Batte, Prosper Kaggwa
For integers , the -generalized Lucas sequence is defined by the recurrence relation \[ L_n^{(k)} = L_{n-1}^{(k)} + \cdots + L_{n-k}^{(k)}…
math.NT2024
Perrin numbers that are palindromic concatenations of two repdigits
Herbert Batte, Prosper Kaggwa
Let be the sequence of Perrin numbers defined by , , and for all . In this paper, we determine all Perr…