Padovan numbers which are concatenations of three repdigits

Abstract

Padovan sequence is a ternary recurrent sequence defined by the recurrence relation $P_{n+3}=P_{n+1}+P_n$ with initial terms $P_0=P_1=P_2=1.$ In this study it is shown that $114,151,200,265,351,465,616,816,3329,4410,7739,922111$ are the only Padovan numbers which are concatenations of three repdigits.

arXiv comment12 pages