11. (12 points) Take any non-zero natural number. If it is even, divide it by 2; if it is odd, multiply it by 3 and add 1. Under such a transformation, we get a new natural number. If we repeatedly apply this transformation, we get a question: will all natural numbers eventually transform to 1? This is the famous "Collatz Conjecture" in mathematics. If a natural number can transform to 1 through the above transformation, the number of transformations it takes to first reach 1 is called its path length. What is the sum of all natural numbers with a path length of 10 in the "Collatz Conjecture"?
1604
【Answer】Solution: Backtrack from 1



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