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Program to check if N is a Centered heptagonal number
  • Last Updated : 07 Apr, 2021

Given an integer N, the task is to check if it is a Centered heptagonal number or not.
 

Centered heptagonal number is centered figure number that represents a heptagon with dot in center and all other dot surrounding in heptagonal form..The first few Centered heptagonal number are 1, 8, 22, 43, 71, 106, 148, …

Examples: 
 

Input: N = 8 
Output: Yes 
Explanation: 
8 is the Second Centered heptagonal number.
Input: 20 
Output: No 
Explanation: 
20 is not a Centered heptagonal number. 
 

 



Approach: 
To solve the problem mentioned above we have to know that the Kth term of the Centered heptagonal number is given as: K^{th} Term = \frac {7*N^{2} - 7*N + 2}{2}
As we have to check that the given number can be expressed as a Centered heptagonal number or not. This can be checked by generalizing the equation as: 
 

=> N = \frac {7*k^{2} - 7*k + 2}{2}
=> K = \frac{7 + \sqrt{56*N + 7}}{14}
 

Finally, check the value of computation using this formula if it is an integer, if yes then it means that N is a Centered heptagonal number.
Below is the implementation of the above approach:
 

C++




// C++ implementation to check that
// a number is a Centered
// heptagonal number or not
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check that the
// number is a Centered
// heptagonal number
bool isCenteredheptagonal(int N)
{
    float n = (7 + sqrt(56 * N - 7)) / 14;
 
    // Condition to check if the
    // number is a Centered heptagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    int n = 8;
 
    // Function call
    if (isCenteredheptagonal(n)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java




// Java implementation to check that
// a number is a Centered
// heptagonal number or not
import java.lang.Math;
 
class GFG
{
     
// Function to check that the
// number is a Centered
// heptagonal number
public static boolean isCenteredheptagonal(int N)
{
    double n = (7 + Math.sqrt(56 * N - 7)) / 14;
 
    // Condition to check if the
    // number is a Centered heptagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 8;
 
    // Function call
    if (isCenteredheptagonal(n))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by divyeshrabadiya07

Python3




# Python3 implementation to check
# that a number is a centered
# heptagonal number or not
import math
 
# Function to check that the
# number is a centered
# heptagonal number
def isCenteredheptagonal(N):
     
    n = (7 + math.sqrt(56 * N - 7)) / 14
     
    # Condition to check if the number
    # is a centered heptagonal number
    return (n - int(n)) == 0
     
# Driver Code
n = 8
 
# Function call
if (isCenteredheptagonal(n)):
    print("Yes")
else:
    print("No")
     
# This code is contributed by ShubhamCoder

C#




// C# implementation to check that
// a number is a centered
// heptagonal number or not
using System;
 
class GFG{
 
// Function to check that the
// number is a centered
// heptagonal number
static bool isCenteredheptagonal(int N)
{
    double n = (7 + Math.Sqrt(56 * N - 7)) / 14;
     
    // Condition to check if the number
    // is a centered heptagonal number
    return (n - (int)n) == 0;
}
     
// Driver Code
static public void Main ()
{
    int n = 8;
     
    // Function call
    if (isCenteredheptagonal(n))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by ShubhamCoder

Javascript




<script>
// Javascript implementation to check that
// a number is a Centered
// heptagonal number or not
 
// Function to check that the
// number is a Centered
// heptagonal number
function isCenteredheptagonal(N)
{
    let n = (7 + Math.sqrt(56 * N - 7)) / 14;
 
    // Condition to check if the
    // number is a Centered heptagonal number
    return (n - parseInt(n)) == 0;
}
 
// Driver Code
let n = 8;
 
// Function call
if (isCenteredheptagonal(n)) {
    document.write("Yes");
}
else {
    document.write("No");
}
 
// This code is contributed by rishavmahato348.
</script>
Output: 
Yes

 

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