Problem 197

Investigating the behaviour of a recursively defined sequence

Given is the function f(x) = ⌊2^{30.403243784-x²}⌋ × 10^-9 ( ⌊ ⌋ is the floor-function),
the sequence u_n is defined by u₀ = -1 and u_n+1 = f(u_n).

Find u_n + u_n+1 for n = 10¹².
Give your answer with 9 digits after the decimal point.

关于一个递归定义序列的研究

已知函数f(x) = ⌊2^{30.403243784-x²}⌋ × 10^-9 （其中⌊ ⌋是下取整函数），
序列u_n定义为u₀ = -1且u_n+1 = f(u_n)。

求u_n + u_n+1，其中n = 10¹²。
你的答案需要保留小数点后9位数字。