Consider the following set of transformations on a given natural number written in base 10:
1) Put a zero at the end 2) Put a 4 at the end 3) Divide it in half
For instance, by applying the sequence 3313 we can change 4 into 5: 4 -> 2 -> 1 -> 10 -> 5. Given a number up to 100,000, this Demonstration shows the steps to reach it from 4 following these transformations. Can you find a number that needs 53 steps?