Investigating the behaviour of a recursively defined sequence
Problem 197Published on Friday, 6th June 2008, 10:00 pm; Solved by 3410; Difficulty rating: 45%
Given is the function f(x) = ⌊230.403243784-x2⌋ × 10-9 ( ⌊ ⌋ is the floor-function),
the sequence un is defined by u0 = -1 and un+1 = f(un).
Find un + un+1 for n = 1012.
Give your answer with 9 digits after the decimal point.