C loop stopping variable from incrementing

Question

I recently learned about Collatz's conjecture. I found it fun, so I just wanted to find out if I could create a small program in C capable of checking the numbers up to a defined number and turned out I wasn't. Here is my program

#include <stdlib.h>
#include <stdio.h>

int main()
{
    int n = 5;
    int u;

    for (int i = 0; i < 1000; i++) {
        while(n != 4) {
            u = n;

            if (n % 2 == 0) {
                n = n / 2;
            }
            else {
                n = 3 * n + 1;
            }
        }

        n = u + 1;
        printf("%d verifies the conjecture \n", n);
    }
}

Problem: The output only shows 9's, and won't increment further. I've done the logic (following what my program would do) by hand, and it works, so I'm completely stumped. Let it be reminded that I'm not good in C, I'm still learning, so it's normal if I'm ignorant to really basic things, as I'm learning it as I go. Thanks all.