The 4 Puzzle

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?


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