1986 AIME Problem 7

The increasing sequence 1,3,4,9,10,12,13\cdots consists of all those positive integers which are powers of 3 or sums of distinct powers of 3. Find the 100^{\text{th}} term of this sequence.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.