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Program to check if N is a Tridecagonal Number or not
  • Last Updated : 15 Mar, 2021

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

Tridecagon number is a thirteen-sided polygon. The first few Tridecagon numbers are 1, 13, 36, 70, 115, 171, …

Examples: 
 

Input: N = 13 
Output: Yes 
Explanation: 
Second Tridecagon number is 13.
Input: N = 30 
Output: No 
 

 



Approach: 
 

  1. The Kth term of the Tridecagon number is given as
    K^{th} Term = \frac{11*K^{2} - 9*K}{2}
     
  2. As we have to check that the given number can be expressed as a Tridecagon number or not. This can be checked as follows – 
     

=> N = \frac{11*K^{2} - 9*K}{2}
=> K = \frac{9 + \sqrt{88*N + 81}}{22}
 

  1.  
  2. Finally, check the value of computed using this formulae is an integer, which means that N is a Tridecagon number.

Below is the implementation of the above approach:
 

C++




// C++ implementation to check that
// a number is a Tridecagon number or not
 
#include <bits/stdc++.h>
 
using namespace std;
 
// Function to check that the
// number is a Tridecagon number
bool isTridecagon(int N)
{
    float n
        = (9 + sqrt(88 * N + 81))
          / 22;
 
    // Condition to check if the
    // number is a Tridecagon number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    int i = 13;
 
    // Function call
    if (isTridecagon(i)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java




// Java implementation to check that a
// number is a tridecagon number or not
class GFG{
 
// Function to check that the
// number is a tridecagon number
static boolean isTridecagon(int N)
{
    float n = (float) ((9 + Math.sqrt(88 * N +
                                      81)) / 22);
 
    // Condition to check if the
    // number is a tridecagon number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void main(String[] args)
{
    int i = 13;
 
    // Function call
    if (isTridecagon(i))
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python3 implementation to check that
# a number is a tridecagon number or not
import math
 
# Function to check that the
# number is a tridecagon number
def isTridecagon(N):
 
    n = (9 + math.sqrt(88 * N + 81)) / 22
 
    # Condition to check if the
    # number is a tridecagon number
    return (n - int(n)) == 0
 
# Driver Code
i = 13
 
# Function call
if (isTridecagon(i)):
    print("Yes")
else:
    print("No")
         
# This code is contributed by divyamohan123

C#




// C# implementation to check that a
// number is a tridecagon number or not
using System;
 
class GFG{
 
// Function to check that the
// number is a tridecagon number
static bool isTridecagon(int N)
{
    float n = (float)((9 + Math.Sqrt(88 * N +
                                     81)) / 22);
 
    // Condition to check if the
    // number is a tridecagon number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void Main()
{
    int i = 13;
 
    // Function call
    if (isTridecagon(i))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by Code_Mech

Javascript




<script>
 
// JavaScript implementation to check that
// a number is a Tridecagon number or not
 
// Function to check that the
// number is a Tridecagon number
function isTridecagon(N)
{
    var n
        = (9 + Math.sqrt(88 * N + 81))
          / 22;
 
    // Condition to check if the
    // number is a Tridecagon number
    return (n - parseInt(n)) == 0;
}
 
// Driver Code
var i = 13;
// Function call
if (isTridecagon(i)) {
    document.write("Yes");
}
else {
    document.write("No");
}
 
</script>
Output: 
Yes

 

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