MathDB

Sequence with floor

Source: Baltic Way 2022, Problem 2

November 12, 2022

algebra

Problem Statement

We define a sequence of natural numbers by the initial values

a_0 = a_1 = a_2 = 1

and the recursion

a_n = \bigg \lfloor \frac{n}{a_{n-1}a_{n-2}a_{n-3}} \bigg \rfloor

for all

n \ge 3

. Find the value of

a_{2022}