Skip to content
Related Articles
Program to check if N is a Pentadecagonal Number
• Last Updated : 15 Mar, 2021

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

Pentadecagon Number is a 15-sided polygon..The first few Pentadecagon numbers are 1, 15, 42, 82, 135, 201, …

Examples:

Input: N = 15
Output: Yes
Explanation:
Second Pentadecagon number is 15.
Input: N = 30
Output: No

Approach:

1. The Kth term of the Pentadecagon number is given as 2. As we have to check that the given number can be expressed as a Pentadecagon Number or not. This can be checked as:

=> => 1.
2. If the value of K calculated using the above formula is an integer, then N is a Pentadecagon Number.
3. Else N is not a Pentadecagon Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach#include using namespace std; // Function to check if N is a// Pentadecagon numberbool isPentadecagon(int N){    float n        = (11 + sqrt(104 * N + 121))          / 26;     // Condition to check if the    // number is a Pentadecagon number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 15;     // Function call    if (isPentadecagon(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.io.*;import java.util.*; class GFG { // Function to check if N is// a pentadecagon numberpublic static boolean isPentadecagon(int N){    double n = (11 + Math.sqrt(104 * N +                               121)) / 26;         // Condition to check if the number    // is a pentadecagon number    return (n - (int)n) == 0;} // Driver codepublic static void main(String[] args){         // Given Number    int N = 15;         // Function call    if (isPentadecagon(N))    {        System.out.println("Yes");    }    else    {        System.out.println("No");    }}} // This code is contributed by coder001

## Python3

 # Python3 program for the above approachfrom math import sqrt # Function to check if N is a# pentadecagon numberdef isPentadecagon(N):     n = (11 + sqrt(104 * N + 121)) / 26;         # Condition to check if the    # number is a pentadecagon number    return (n - int(n) == 0); # Driver Codeif __name__ == "__main__":     # Given number    N = 15;     # Function call    if (isPentadecagon(N)):        print("Yes");         else :        print("No");     # This code is contributed by AnkitRai01

## C#

 // C# program for the above approachusing System; class GFG { // Function to check if N is// a pentadecagon numberpublic static bool isPentadecagon(int N){    double n = (11 + Math.Sqrt(104 * N +                               121)) / 26;         // Condition to check if the number    // is a pentadecagon number    return (n - (int)n) == 0;} // Driver codepublic static void Main(String[] args){         // Given Number    int N = 15;         // Function call    if (isPentadecagon(N))    {        Console.WriteLine("Yes");    }    else    {        Console.WriteLine("No");    }}} // This code is contributed by Amit Katiyar

## Javascript

 
Output:
Yes

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer DSA Live Classes

My Personal Notes arrow_drop_up