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

Authors: JHON JAIRO BRAVO, MARIBEL DÍAZ, JOSÉ LUIS RAMÍREZ

Abstract: Let $(T_n)_{n\geq 0}$ denote the Tripell sequence, defined by the linear recurrence $T_n=2T_{n-1} + T_{n-2}+T_{n-3}$ for $n\geq 3$ with $T_0=0$, $T_{1}=1$ and $T_2=2$ 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.

Keywords: Tripell sequence, $p$-adic valuation, factorials

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