yaworsw/euler-manager

---
:id: 197
:name: Investigating the behaviour of a recursively defined sequence
:url: https://projecteuler.net/problem=197
:content: "Given is the function <var>f</var>(<var>x</var>) = ⌊2<sup>30.403243784-<var>x</var><sup>2</sup></sup>⌋
  × 10<sup>-9</sup> ( ⌊ ⌋ is the floor-function),  \nthe sequence <var>u<sub>n</sub></var>
  is defined by <var>u</var><sub>0</sub> = -1 and <var>u</var><sub><var>n</var>+1</sub>
  = <var>f</var>(<var>u<sub>n</sub></var>).\n\nFind <var>u<sub>n</sub></var> + <var>u</var><sub><var>n</var>+1</sub>
  for <var>n</var> = 10<sup>12</sup>.  \nGive your answer with 9 digits after the
  decimal point.\n\n"