I'm tinkering a bit with Java but have a lot of experience in some other languages. I have a test problem that I know solution to (and can easily produce in Python and C++). But running the following Java code gives an

Exception in thread "main" java.lang.OutOfMemoryError: Java heap space

I'm wondering if I'm making a simple mistake, I would not expect the memory footprint of this program to be very large at all:

public static void main(String[] args) {
    ArrayList<Integer> longest_sequence = new ArrayList<>();
    ArrayList<Integer> this_sequence;
    int n = 0;

    for (int i = 1; i < 1000000; i++) {
        this_sequence = new ArrayList<Integer>();

        n = i;
        this_sequence.add(n);
        while (n != 1) {
            if (n % 2 == 0) {
                n = n / 2;
            }
            else {
                n = 3*n + 1;
            }
            this_sequence.add(n);
        }
        if (this_sequence.size() > longest_sequence.size()) {
            longest_sequence = this_sequence;
        }
    }

    System.out.println(longest_sequence.get(0));
    System.out.println(longest_sequence.size());

}

To clarify a bit more:

A new list is created in each iteration of the program. It is either kept by assigning the longest_sequence to it, or it is discarded and overwritten by a new list instance.

I'm guessing my assumptions about that are incorrect, and instances are being preserved? The size of the lists should not be a problem (about 500 elements for the largest one).