# How many two's?

Level pending

Define $$f(x)=3^{2^x}-1$$. Define $$g(x)$$ as the largest number $$n$$ such that $$\dfrac{f(x)}{2^n}$$ is a positive integer. Find the last three digits of $$\displaystyle\sum^{2014}_{i=0}{g(x)}$$.

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