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Program to check if N is a Heptadecagonal Number
• Last Updated : 08 Apr, 2021

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

Heptadecagonal Number is class of figurate number. It has 17-sided polygon called heptadecagon. The N-th heptadecagonal number counts the seventeen number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few heptadecagonal numbers are 1, 17, 48, 94, 155, 231…

Examples:

Input: N = 17
Output: Yes
Explanation:
Second heptadecagonal number is 17.

Input: N = 30
Output: No

Approach:

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

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

4. Else N is not a Heptadecagonal Number.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach#include using namespace std; // Function to check if the number N// is a heptadecagonal numberbool isheptadecagonal(int N){    float n        = (13 + sqrt(120 * N + 169))          / 30;     // Condition to check if number N    // is a heptadecagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 17;     // Function call    if (isheptadecagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.util.*; class GFG{ // Function to check if the number N// is a heptadecagonal numberstatic boolean isheptadecagonal(int N){    float n = (float) ((13 + Math.sqrt(120 * N +                                       169)) / 30);     // Condition to check if number N    // is a heptadecagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void main(String[] args){         // Given Number    int N = 17;     // Function call    if (isheptadecagonal(N))    {        System.out.print("Yes");    }    else    {        System.out.print("No");    }}} // This code is contributed by Amit Katiyar

## Python3

 # Python3 program for the above approachimport numpy as np # Function to check if the number N# is a heptadecagonal numberdef isheptadecagonal(N):     n = (13 + np.sqrt(120 * N + 169)) / 30     # Condition to check if number N    # is a heptadecagonal number    return (n - int(n)) == 0 # Driver CodeN = 17 # Function callif (isheptadecagonal(N)):    print("Yes")else:    print("No") # This code is contributed by PratikBasu

## C#

 // C# program for the above approachusing System; class GFG{ // Function to check if the number N// is a heptadecagonal numberstatic bool isheptadecagonal(int N){    float n = (float) ((13 + Math.Sqrt(120 * N +                                       169)) / 30);     // Condition to check if number N    // is a heptadecagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void Main(string[] args){         // Given Number    int N = 17;     // Function call    if (isheptadecagonal(N))    {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}} // This code is contributed by rutvik_56

## Javascript

 
Output:
Yes

Time Complexity: O(1)

Auxiliary Space: O(1)

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