What are the positive integers x for which
I am not good enough to prove it, but the answers are going to be 2 and 3.
After this, the (x+3)^x begins to outpace the sum of the lower powers, so it will continue to grow at a faster rate, and they won't ever catch back up. You can see it by charting the next few but like I said, I'm not good enough to prove it. Maybe someone else can prove it, I would love to see their thought process.