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# Program to check if N is a Tridecagonal Number or not

• Last Updated : 23 Jun, 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

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 –

=>
=>

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  using namespace std; // Function to check that the// number is a Tridecagon numberbool 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 Codeint 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 notclass GFG{ // Function to check that the// number is a tridecagon numberstatic 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 Codepublic 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 notimport math # Function to check that the# number is a tridecagon numberdef 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 Codei = 13 # Function callif (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 notusing System; class GFG{ // Function to check that the// number is a tridecagon numberstatic 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 Codepublic 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

 
Output:
Yes

Time Complexity: O(1)

Auxiliary Space: O(1)

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