The 2-adic and 3-adic valuation of the Tripell sequence and an application

Abstract

Let (Tn)n≥0 denote the Tripell sequence, defined by the linear recurrence Tn=2Tn−1+Tn−2+Tn−3 for n≥3 with T0=0, T1=1 and T2=2 as initial conditions. In this paper, we study the 2-adic and 3-adic valuation of the Tripell sequence and, as an application, we determine all Tripell numbers which are factorials.