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One needs to decide on some balance between the cost of storing and the cost of computing. Find out what values are worth storing and will make other calculations easier. This might depend on $f$.

Would storing the values at primes or prime powers make more sense? Values at multiple of $2^{30}$?

In any case, $10^{1000}$ is a lot, there is not much hope to compute $f(n)$ for all values of $n$ up to that bound.