With Greater Powers

\[4, 2+2, 2+1+1, 1+2+1, 1+1+2, 1+1+1+1\]

Let \(f(n)\) be the number of ways in which one can express \(n\) as the sum of powers of \(2\), where each permutation is distinct. For example, \(f(4) = 6\) because \(4\) can be written in the 6 ways listed above.

Find the smallest \(n\) greater than \(2013\) for which \(f(n)\) is odd.

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