Codeforces Round #372 (Div. 1) A. Plus and Square Root 数学题

A. Plus and Square Root

题目连接：

http://codeforces.com/contest/715/problem/A

Description

ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at the level 1.

When ZS the Coder is at level k, he can :

Press the ' + ' button. This increases the number on the screen by exactly k. So, if the number on the screen was x, it becomes x + k.
Press the '' button. Let the number on the screen be x. After pressing this button, the number becomes . After that, ZS the Coder levels up, so his current level becomes k + 1. This button can only be pressed when x is a perfect square, i.e. x = m2 for some positive integer m.

Additionally, after each move, if ZS the Coder is at level k, and the number on the screen is m, then m must be a multiple of k. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level 4 and current number is 100, he presses the '' button and the number turns into 10. Note that at this moment, 10 is not divisible by 4, but this press is still valid, because after it, ZS the Coder is at level 5, and 10 is divisible by 5.

ZS the Coder needs your help in beating the game — he wants to reach level n + 1. In other words, he needs to press the '' button n times. Help him determine the number of times he should press the ' + ' button before pressing the '' button at each level.

Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level n + 1, but not necessarily a sequence minimizing the number of presses.

Input

The first and only line of the input contains a single integer n (1 ≤ n ≤ 100 000), denoting that ZS the Coder wants to reach level n + 1.

Output

Print n non-negative integers, one per line. i-th of them should be equal to the number of times that ZS the Coder needs to press the ' + ' button before pressing the '' button at level i.

Each number in the output should not exceed 1018. However, the number on the screen can be greater than 1018.

It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.

Sample Input

4

Sample Output

2

17

46

97

Hint

题意

一开始屏幕上是x，然后你有两个操作

操作一是让数字加上(x-1)

操作二是让数字开根号，但是数字开根号后，必须是x的倍数

现在假设一开始屏幕上数字是2，你想让数字变成n+1，问你每一步你需要进行操作一多少次。

题解：

数学题，每次把最小的那个满足的数字拿出来，就会发现有规律，然后输出就好了。

代码

#include<bits/stdc++.h>
using namespace std;

int main()
{
    int n;
    scanf("%d",&n);
    cout<<"2"<<endl;
    for(int i=2;i<=n;i++)
        cout<<1ll*i*(i+1)*(i+1)-i+1<<endl;
}