Mudit and Sequences

Mudit is interested in sequences. He also has preferences for numbers. He thinks n integers a1, a2, ..., an are special. Now he is interested in special sequences. A sequence x(1), x(2), ..., x(k) is called special if it satisfies the following three conditions: -- The sequence is strictly increasing, that is x(i) < x(i+1) for each i (1 <= i <= k-1). -- No two adjacent elements are co-pri