Program to check if N is a Centered Tridecagonal Number

Last Updated : 19 Sep, 2022

Given a number N, the task is to check if N is a Centered Tridecagonal Number or not. If the number N is a Centered Tridecagonal Number then print “Yes” else print “No”.

Centered tridecagonal number represents a dot at the center and other dots surrounding the center dot in the successive tridecagonal(13 sided polygon) layer. The first few Centered tridecagonal numbers are 1, 14, 40, 79 …

Examples:

Input: N = 14
Output: Yes
Explanation:
Second Centered tridecagonal number is 14.

Input: N = 30
Output: No

Approach:

1. The K^th term of the Centered Tridecagonal Number is given as
$K^{th} Term = \frac{{13*K^{2} - 13*K + 2}}{2}$

2. As we have to check that the given number can be expressed as a Centered Tridecagonal Number or not. This can be checked as follows:

=> $N = \frac{{13*K^{2} - 13*K + 2}}{2}$
=> $K = \frac{13 + \sqrt{104*N + 65}}{26}$

3. If the value of K calculated using the above formula is an integer, then N is a Centered Tridecagonal Number.

4. Else the number N is not a Centered Tridecagonal Number.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if the number N
// is a Centered tridecagonal number
bool isCenteredtridecagonal(int N)
{
    float n
        = (13 + sqrt(104 * N + 65))
          / 26;
 
    // Condition to check if the N
    // is a Centered tridecagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    // Given Number
    int N = 14;
 
    // Function call
    if (isCenteredtridecagonal(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java program for the above approach
class GFG{
 
// Function to check if the number N
// is a centered tridecagonal number
static boolean isCenteredtridecagonal(int N)
{
    float n = (float) ((13 + Math.sqrt(104 * N + 
                                       65)) / 26);
 
    // Condition to check if the N
    // is a centered tridecagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Given Number
    int N = 14;
 
    // Function call
    if (isCenteredtridecagonal(N))
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
 
// This code is contributed by sapnasingh4991

Python3

# Python3 program for the above approach
import numpy as np
 
# Function to check if the number N
# is a centered tridecagonal number 
def isCenteredtridecagonal(N):
 
    n = (13 + np.sqrt(104 * N + 65)) / 26
 
    # Condition to check if N 
    # is centered tridecagonal number
    return (n - int(n)) == 0
 
# Driver Code 
N = 14
 
# Function call 
if (isCenteredtridecagonal(N)):
    print ("Yes") 
else:
    print ("No")
 
# This code is contributed by PratikBasu

C#

// C# program for the above approach 
using System; 
 
class GFG{ 
 
// Function to check if the number N 
// is a centered tridecagonal number 
static bool isCenteredtridecagonal(int N) 
{ 
    float n = (float) ((13 + Math.Sqrt(104 * N + 
                                       65)) / 26); 
 
    // Condition to check if the N 
    // is a centered tridecagonal number 
    return (n - (int)n) == 0; 
} 
 
// Driver Code 
public static void Main(string[] args) 
{ 
     
    // Given Number 
    int N = 14; 
 
    // Function call 
    if (isCenteredtridecagonal(N)) 
    { 
        Console.Write("Yes"); 
    } 
    else
    { 
        Console.Write("No"); 
    } 
} 
} 
 
// This code is contributed by rutvik_56

Javascript

<script>
// Javascript program for the above approach
 
// Function to check if the number N
// is a Centered tridecagonal number
function isCenteredtridecagonal(N)
{
    let n
        = (13 + Math.sqrt(104 * N + 65))
          / 26;
 
    // Condition to check if the N
    // is a Centered tridecagonal number
    return (n - parseInt(n)) == 0;
}
 
// Driver Code
// Given Number
let N = 14;
 
// Function call
if (isCenteredtridecagonal(N)) {
    document.write("Yes");
}
else {
    document.write("No");
}
 
// This code is contributed by subham348.
</script>

Output:

Yes

Time Complexity: O(logN) since inbuilt sqrt function is being used

Auxiliary Space: O(1)

Suggest improvement

Program to check if N is a Centered Decagonal Number

Program to check if N is a Centered dodecagonal number

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Program to check if N is a Centered Tridecagonal Number

C++

Java

Python3

C#

Javascript

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