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

Authors

JHON JAIRO BRAVO
MARIBEL DÍAZ
JOSÉ LUIS RAMÍREZ

DOI

10.3906/mat-1907-40

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

First Page

131

Last Page

141

Recommended Citation

BRAVO, JHON JAIRO; DÍAZ, MARIBEL; and RAMÍREZ, JOSÉ LUIS (2020) "The $2$-adic and $3$-adic valuation of the Tripell sequence and an application," Turkish Journal of Mathematics: Vol. 44: No. 1, Article 9. https://doi.org/10.3906/mat-1907-40
Available at: https://journals.tubitak.gov.tr/math/vol44/iss1/9