Narayana’s cows numbers which are concatenations of three repdigits in base ρ

Abstract

Narayana’s sequence is a ternary recurrent sequence defined by the recurrence relation [Formula: see text] with initial terms [Formula: see text] and [Formula: see text]. Let [Formula: see text] be a positive integer. In this study, it is proved that the [Formula: see text]th Narayana’s number [Formula: see text] which is concatenations of three repdigits in base [Formula: see text] satisfies [Formula: see text]. Moreover,it is shown that the largest Narayana’s number which is concatenations of three repdigits in base [Formula: see text] with [Formula: see text] is [Formula: see text].