Given is the function $f(x) = \lfloor 2^{30.403243784 - x^2}\rfloor \times 10^{-9}$ ($\lfloor \, \rfloor$ is the floor-function),
the sequence $u_n$ is defined by $u_0 = -1$ and $u_{n + 1} = f(u_n)$.
Find $u_n + u_{n + 1}$ for $n = 10^{12}$.
Give your answer with $9$ digits after the decimal point.
Solution
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