Dio-sequence (Part 1)

Algebra Level pending

A strictly increasing sequence of positive integers \(a_1\), \(a_2\), \(a_3\),... has the property that for every positive integer \(k\), the subsequence \(a_{2k-1}\), \(a_{2k}\), \(a_{2k+1}\) is geometric and the subsequence \(a_{2k}\), \(a_{2k+1}\), \(a_{2k+2}\) is arithmetic. If \(a_{13}=2016\), compute \(a_1\).

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