# A very base-ic problem

Consider a sequence, where the $$n$$-th term is the smallest positive integer such that when it is written in base $$k$$ representation, it only consists of the digits 1's and 0's, where $$k = 2, 3, \ldots, n+1$$.

For example, since $$2 = 10_2$$ and $$3 = 11_2 = 10_3$$ and $$4 = 100_2 = 11_3 = 10_4$$, hence the first three terms of the sequence is $$2,3,4$$.

What is the fourth number in this sequence? Give your answer in decimal representation.

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