On the 3-adic valuation of the Narayana numbers

2021/12/12 by Guadalupe, Russelle · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.06187

Abstract

We define the Narayana sequence \a_n\_{n≥ 0} as the one satisfying the linear recurrence relation a_n = a_n-1+a_n-3 for n≥ 3, with initial values a₀ = 0 and a₁ = a₂=1. In this paper, we fully characterize the 3-adic valuation of a_n and use this to determine all Narayana numbers that are factorials.

Cited by

• Residues of Terms of Lucas Sequences Modulo 3^k

Related

• Narayana Sequence and The Brocard-Ramanujan Equation
• Narayana's cows numbers which are concatenations of three repdigits in base ρ
• Identities involving Narayana numbers
• Narayana numbers as product of three repdigits in base g
• Repdigits in Narayana's Cows Sequence and their Consequences