# 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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