Problem

Source: CSMO 2019 Grade 11 Problem 3

Tags: combinatorics



$n$ symbols line up in a row, numbered as $1,2,...,n$ from left to right. Delete every symbol with squared numbers. Renumber the rest from left to right. Repeat the process until all $n$ symbols are deleted. Let $f(n)$ be the initial number of the last symbol deleted. Find $f(n)$ in terms of $n$ and find $f(2019)$.