A strictly increasing sequence of positive integers a_{1}, a_{2}, a_{3}, \ldots has the property that for every positive integer k, the subsequence a_{2 k-1}, a_{2 k}, a_{2 k+1} is geometric and the subsequence a_{2 k}, a_{2 k+1}, a_{2 k+2} is arithmetic. Suppose that a_{13}=2016. Find a_{1}.