Eva lists the positive integers, but skips all numbers containing a digit divisible by $$3$$. For example, the first ten numbers she lists are $$1, 2, 4, 5, 7, 8, 11, 12, 14, 15$$. What is the $$100^{\text{th}}$$ number in her list?

This problem is shared by Muhammad A.

Details and assumptions

The number $$13$$ is not included in the list, since it contains the digit 3, which is divisible by 3.

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