2020 AIME II Problem 8

Define a sequence recursively by f_1(x)=|x-1| and f_n(x)=f_{n-1}(|x-n|) for integers n>1. Find the least value of n such that the sum of the zeros of f_n exceeds 500,000.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.