## Investigating the behaviour of a recursively defined sequence

### Problem 197

Published on Friday, 6th June 2008, 10:00 pm; Solved by 3376; Difficulty rating: 45%Given is the function `f`(`x`) = ⌊2^{30.403243784-x2}⌋ × 10^{-9} ( ⌊ ⌋ 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.