Let f ∶ N → R be a function such that f(x + y) = 2 f(x) f(y) for natural numbers x and y. If f(1) = 2, then the value of "α" for which \(\displaystyle\sum_{k=1}^{10}\)f(α + k) = \(\frac{512}{3}\)(2²⁰ − 1) holds, is :