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.

This is not an original problem.
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