# Solution of;
# Project Euler Problem 656: Palindromic sequences
# https://projecteuler.net/problem=656
# 
# Given an irrational number $\alpha$, let $S_\alpha(n)$ be the sequence 
# $S_\alpha(n)=\lfloor {\alpha \cdot n} \rfloor - \lfloor {\alpha \cdot (n-1)} 
# \rfloor$ for $n \ge 1$. ($\lfloor . . . \rfloor$ is the floor-function. )It 
# can be proven that for any irrational $\alpha$ there exist infinitely many 
# values of $n$ such that the subsequence $ \{S_\alpha(1),S_\alpha(2). . . 
# S_\alpha(n) \} $ is palindromic. The first 20 values of $n$ that give a 
# palindromic subsequence for $\alpha = \sqrt{31}$ are:1, 3, 5, 7, 44, 81, 
# 118, 273, 3158, 9201, 15244, 21287, 133765, 246243, 358721, 829920, 9600319, 
# 27971037, 46341755, 64712473. Let $H_g(\alpha)$ be the sum of the first $g$ 
# values of $n$ for which the corresponding subsequence is palindromic. So 
# $H_{20}(\sqrt{31})=150243655$. Let $T=\{2,3,5,6,7,8,10,. . . ,1000\}$ be the 
# set of positive integers, not exceeding 1000, excluding perfect squares. 
# Calculate the sum of $H_{100}(\sqrt \beta)$ for $\beta \in T$. Give the last 
# 15 digits of your answer.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 656
    timed.caller(dummy, n, i, prob_id)
