For a positive integer N, box(N) is defined as N/2 if N is even, and 3N + 1 if N is odd. What is the value of box(2009) - box(2008)?
Your question is a major mathematical conjecture, still unsolved, and is called the "Collatz Conjecture".
Box(2009), n = 1 after 24 steps
Box(2008), n = 1 after 68 steps.
Each term in this question is NOT derived from the previous term so it is not Collatz conjecture.
"The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1."