Let $a_1 < a_2 < a_3 < \ldots < a_n < \ldots$ be positive integers such that, for $n = 1, 2, 3, \ldots,$  
\[ a_{2n} = a_n + n. \]  
Given that if $a_n$ is prime, then $n$ is also, find $a_{2014}$.

Let's think step by step and output the final answer within \boxed{}.
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