检查数字是否为Flavius数

给定一系列从1到无穷大的整数，以及一个数N。

任务是在第i次迭代中从其余序列中删除第(i +1)个元素，并确定给定数字N是否存在于序列中。

黄蜂编号：

Numbers in the Flavius Sieve are called Flavius Numbers.

Flavius sieve starts with the natural numbers and keep repeating the below step:
At the k-th sieving step, remove every (k+1)-st term of the sequence remaining of N natural numbers after the (k-1)-st sieving step.

For Example: 1, 3, 7, 13, 19, 27, 39, 49,

例子：

Input: N = 17
Output: N0

Series after i-th iterations
1). 1, 3, 5, 7, 9, 11, 13, 15, 17, …
2). 1, 3, 7, 9, 13, 15, 19, 21, 25, …
3). 1, 3, 7, 13, 15, 19, 25, …
4). 1, 3, 7, 13, 19, 27, ….

Input: N = 3
Output: Yes

方法：

• 如果给定的数字是偶数，那么答案就是“否”。因为在第一次迭代中，所有偶数都已从序列中消除。
• 重复此过程。
  • 否则，删除第一次迭代中删除的元素数量，即第(1/2)个数量，然后检查
    如果可以被3整除，则答案应该为“否”，否则减去之前的数字
    删除编号的(1/3)，依此类推。
  • 对所有迭代重复上述步骤，直到得到答案。

下面是该方法的实现：

C++

// C++ implementation
#include 
using namespace std;
  
// Return the number is
// Flavious Number or not
bool Survives(int n)
{
    int i;
  
    // index i starts from 2 because
    // at 1st iteration every 2nd
    // element was remove and keep
    // going for k-th iteration
    for (int i = 2;; i++) {
        if (i > n)
            return true;
        if (n % i == 0)
            return false;
  
        // removing the elements which are
        // already removed at kth iteration
        n -= n / i;
    }
}
  
// Driver Code
int main()
{
    int n = 17;
    if (Survives(n))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
  
    return 0;
}

Java

// Java implementation of the above approach
class GFG 
{
  
// Return the number is
// Flavious Number or not
static boolean Survives(int n)
{
  
    // index i starts from 2 because
    // at 1st iteration every 2nd
    // element was remove and keep
    // going for k-th iteration
    for (int i = 2;; i++)
    {
        if (i > n)
            return true;
        if (n % i == 0)
            return false;
  
        // removing the elements which are
        // already removed at kth iteration
        n -= n / i;
    }
}
  
// Driver Code
public static void main(String[] args)
{
    int n = 17;
    if (Survives(n))
        System.out.println("Yes");
    else
        System.out.println("No");
}
} 
  
// This code is contributed by 29AjayKumar

Python3

# Python3 implementation of
# the above approach 
  
# Return the number is 
# Flavious Number or not 
def Survives(n) :
  
    # index i starts from 2 because 
    # at 1st iteration every 2nd 
    # element was remove and keep 
    # going for k-th iteration 
    i = 2
    while(True) :
          
        if (i > n) :
            return True; 
              
        if (n % i == 0) :
            return False; 
  
        # removing the elements which are 
        # already removed at kth iteration 
        n -= n // i;
        i += 1
  
# Driver Code 
if __name__ == "__main__" : 
  
    n = 17; 
      
    if (Survives(n)) :
        print("Yes");
          
    else :
        print("No");
          
# This code is contributed by AnkitRai01

C#

// C# implementation of the above approach
using System;
  
class GFG 
{
  
// Return the number is
// Flavious Number or not
static bool Survives(int n)
{
  
    // index i starts from 2 because
    // at 1st iteration every 2nd
    // element was remove and keep
    // going for k-th iteration
    for (int i = 2;; i++)
    {
        if (i > n)
            return true;
        if (n % i == 0)
            return false;
  
        // removing the elements which are
        // already removed at kth iteration
        n -= n / i;
    }
}
  
// Driver Code
public static void Main(String[] args)
{
    int n = 17;
    if (Survives(n))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
} 
  
// This code is contributed by PrinciRaj1992

输出：

No