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.