Palindromic concatenations of two distinct repdigits in Narayana's cows sequence
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916076554551296 |
|---|---|
| author | Ddamulira, Mahadi Emong, Paul Mirumbe, Geoffrey Ismail |
| author_facet | Ddamulira, Mahadi Emong, Paul Mirumbe, Geoffrey Ismail |
| contents | Let $(N_{n})_{n\ge 0}$ be Narayana's cows sequence given by a recurrence relation $ N_{n+3}=N_{n+2}+N_n $ for all $ n\ge 0 $, with initial conditions $ N_0=0 $, and $ N_1= N_2=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 $10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17571 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Palindromic concatenations of two distinct repdigits in Narayana's cows sequence Ddamulira, Mahadi Emong, Paul Mirumbe, Geoffrey Ismail Number Theory 11B37 11D61 11J86 Let $(N_{n})_{n\ge 0}$ be Narayana's cows sequence given by a recurrence relation $ N_{n+3}=N_{n+2}+N_n $ for all $ n\ge 0 $, with initial conditions $ N_0=0 $, and $ N_1= N_2=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 $10$. |
| title | Palindromic concatenations of two distinct repdigits in Narayana's cows sequence |
| topic | Number Theory 11B37 11D61 11J86 |
| url | https://arxiv.org/abs/2312.17571 |