# Program to check if N is a Enneadecagonal Number

• Last Updated : 12 Apr, 2021

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

Enneadecagonal Number is a 19-sided polygon in mathematics. It belongs to a class of figurative number. The number contains the number of dots and the dots are arranged in a pattern or series. An Enneadecagonal Number is also known as Nonadecagon. The dots have common points and all other dots are arrange in the successive layer. The nth Enneadecagonal Number counts the seventeen number of dots and all the other dots are surrounding with a common sharing corner and make a pattern. The first few Enneadecagonal Numbers are 1, 19, 54, 106, 175…

Examples:

Input: N = 19
Output: Yes
Explanation:

Input: N = 30
Output: No

Approach:

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

=> => 3. If the value of K calculated using the above formula is an integer, then N is a Enneadecagonal Number.

4. Else N is not a Enneadecagonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach #include  using namespace std;   // Function to check if number N // is a enneadecagonal number bool isenneadecagonal(int N) {     float n         = (15 + sqrt(136 * N + 225))           / 34;       // Condition to check if N is a     // enneadecagonal number     return (n - (int)n) == 0; }   // Driver Code int main() {     // Given Number     int N = 19;       // Function call     if (isenneadecagonal(N)) {         cout << "Yes";     }     else {         cout << "No";     }     return 0; }

## Java

 // Java program for the above approach class GFG{   // Function to check if number N // is a enneadecagonal number static boolean isenneadecagonal(int N) {     float n = (float)(15 + Math.sqrt(136 * N +                                      225)) / 34;       // Condition to check if N is a     // enneadecagonal number     return (n - (int)n) == 0; }   // Driver Code public static void main(String[] args) {           // Given Number     int N = 19;       // Function call     if (isenneadecagonal(N))     {         System.out.println("Yes");     }     else     {         System.out.println("No");     } } }   // This code is contributed by rutvik_56

## Python3

 # Python3 program for the above approach  import math   # Function to check if number N  # is a enneadecagonal number  def isenneadecagonal(N):       n = (15 + math.sqrt(136 * N + 225)) / 34       # Condition to check if N is a      # enneadecagonal number      return (n - int(n)) == 0   # Driver Code  N = 19   # Function call  if (isenneadecagonal(N)):     print("Yes")  else:      print("No")    # This code is contributed by divyamohan123

## C#

 // C# program for the above approach using System;   class GFG{   // Function to check if number N // is a enneadecagonal number static bool isenneadecagonal(int N) {     float n = (float)(15 + Math.Sqrt(136 * N +                                      225)) / 34;           // Condition to check if N is a     // enneadecagonal number     return (n - (int)n) == 0; }       // Driver Code static public void Main () {               // Given number     int N = 19;           // Function call     if (isenneadecagonal(N))     {         Console.Write("Yes");     }     else     {         Console.Write("No");     } } }   // This code is contributed by shubhamsingh10

## Javascript

 

Output:

Yes

Time Complexity: O(1)

Auxiliary Space: O(1)

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