I am trying to solve the same problem as asked [here.](https://math.stackexchange.com/q/110868/45001)

In short, I am trying to find the values for which
$$8n^2 \lt 64n\,\log\_2(n)$$

To find a solution in the real numbers, it involves using the Lambert W function, but as the domain of the functions is limited to the natural numbers [this answer](https://math.stackexchange.com/a/110872/45001) suggests "do it numerically".

If this means plugging integers into the two functions and finding the values for which the inequality holds, **how should I approach the selection of the integers?**

How can I tackle this problem more efficiently than just picking numbers from the air?