Program to check if N is a Heptadecagonal Number

Given an integer N, the task is to check if it is a Heptadecagonal Number or not. If the number N is an Heptadecagonal Number then print “Yes” else print “No”.

Heptadecagonal Number is class of figurate number. It has 17-sided polygon called heptadecagon. The N-th heptadecagonal number counts the seventeen number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few heptadecagonal numbers are 1, 17, 48, 94, 155, 231…

Examples:

Input: N = 17
Output: Yes
Explanation:
Second heptadecagonal number is 17.

Input: N = 30
Output: No



Approach:

  1. The Kth term of the heptadecagonal number is given as

    K^{th} Term =  \frac{15*K^{2} - 13*K}{2}

  2. As we have to check that the given number can be expressed as a heptadecagonal number or not. This can be checked as follows –

    => N =  \frac{15*K^{2} - 13*K}{2}
    => K = \frac{13 + \sqrt{120*N + 169}}{30}

  3. If the value of K calculated using the above formula is an integer, then N is a Heptadecagonal Number.
  4. Else N is not a Heptadecagonal Number.

Below is the implementation of the above approach:

C++

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// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to check if the number N
// is a heptadecagonal number
bool isheptadecagonal(int N)
{
    float n
        = (13 + sqrt(120 * N + 169))
          / 30;
  
    // Condition to check if number N
    // is a heptadecagonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
int main()
{
    // Given Number
    int N = 17;
  
    // Function call
    if (isheptadecagonal(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

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Java

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// Java program for the above approach
import java.util.*;
  
class GFG{
  
// Function to check if the number N
// is a heptadecagonal number
static boolean isheptadecagonal(int N)
{
    float n = (float) ((13 + Math.sqrt(120 * N + 
                                       169)) / 30);
  
    // Condition to check if number N
    // is a heptadecagonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
public static void main(String[] args)
{
      
    // Given Number
    int N = 17;
  
    // Function call
    if (isheptadecagonal(N))
    {
        System.out.print("Yes");
    }
    else 
    {
        System.out.print("No");
    }
}
}
  
// This code is contributed by Amit Katiyar

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Python3

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# Python3 program for the above approach 
import numpy as np
  
# Function to check if the number N 
# is a heptadecagonal number 
def isheptadecagonal(N): 
  
    n = (13 + np.sqrt(120 * N + 169)) / 30
  
    # Condition to check if number N 
    # is a heptadecagonal number 
    return (n - int(n)) == 0
  
# Driver Code 
N = 17
  
# Function call 
if (isheptadecagonal(N)):
    print("Yes"
else:
    print("No"
  
# This code is contributed by PratikBasu 

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C#

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// C# program for the above approach
using System;
  
class GFG{
  
// Function to check if the number N
// is a heptadecagonal number
static bool isheptadecagonal(int N)
{
    float n = (float) ((13 + Math.Sqrt(120 * N + 
                                       169)) / 30);
  
    // Condition to check if number N
    // is a heptadecagonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
public static void Main(string[] args)
{
      
    // Given Number
    int N = 17;
  
    // Function call
    if (isheptadecagonal(N))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
  
// This code is contributed by rutvik_56

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Output:

Yes

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