Repdigits as sums of three Padovan numbers

Abstract

Let $\{P_n{\}}_{n\ge 0}$ be the sequence of Padovan numbers defined by $P_0=0$, $P_1=1=P_2$ and $P_{n+3}=P_{n+1}+P_n$ for all $n\ge 0$. In this paper, we find all repdigits in base $10$ which can be written as a sum of three Padovan numbers.

13 pages. arXiv admin note: text overlap with arXiv:1905.11322, arXiv:1906.06330