# Solution of;
# Project Euler Problem 729: Range of periodic sequence
# https://projecteuler.net/problem=729
# 
# Consider the sequence of real numbers $a_n$ defined by the starting value 
# $a_0$ and the recurrence$\displaystyle a_{n+1}=a_n-\frac 1 {a_n}$ for any $n 
# \ge 0$. For some starting values $a_0$ the sequence will be periodic. For 
# example, $a_0=\sqrt{\frac 1 2}$ yields the sequence:$\sqrt{\frac 1 
# 2},-\sqrt{\frac 1 2},\sqrt{\frac 1 2}, \dots$We are interested in the range 
# of such a periodic sequence which is the difference between the maximum and 
# minimum of the sequence. For example, the range of the sequence above would 
# be $\sqrt{\frac 1 2}-(-\sqrt{\frac 1 2})=\sqrt{ 2}$. Let $S(P)$ be the sum 
# of the ranges of all such periodic sequences with a period not exceeding 
# $P$. For example, $S(2)=2\sqrt{2} \approx 2. 8284$, being the sum of the 
# ranges of the two sequences starting with $a_0=\sqrt{\frac 1 2}$ and 
# $a_0=-\sqrt{\frac 1 2}$. You are given $S(3) \approx 14. 6461$ and $S(5) 
# \approx 124. 1056$. Find $S(25)$, rounded to 4 decimal places.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 729
    timed.caller(dummy, n, i, prob_id)
