Play with Exponents

Samuel has n boxes of blue balls to dispatch to his clients. Each of the boxes is numbered from 1 to n, such that the number of blue balls in each box - a(i) is such that a(1), a(2) … a(n) are sorted in non-decreasing order. In a complex encoding of his records that Samuel follows, he writes integers 2a(1), 2a(2), 2a(3) ….. 2a(n) on paper. Now in order to represent this set of boxes, he requires