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.