Related Articles
Program to check if N is a Centered Pentagonal Number or not
• Last Updated : 05 Apr, 2021

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

Centered Pentagonal Number is a centered figurate number that represents a pentagon with a dot in the centre and other dots surrounding it in pentagonal layers successively. The first few Centered Pentagonal Number are 1, 6, 16, 31, 51, 76, 106 …

Examples:

Input: N = 6
Output: Yes
Explanation:
Second Centered pentagonal number is 6.

Input: N = 20
Output: No

Approach:

1. The Kth term of the Centered Pentagonal Number is given as

2. As we have to check that the given number can be expressed as a Centered Pentagonal 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 Centered Pentagonal Number.

4. Else the number N is not a Centered Pentagonal 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 Centered pentagonal numberbool isCenteredpentagonal(int N){    float n        = (5 + sqrt(40 * N - 15))          / 10;     // Condition to check if N is a    // Centered pentagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 6;     // Function call    if (isCenteredpentagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.util.*; class GFG{ // Function to check if number N// is a centered pentagonal numberstatic boolean isCenteredpentagonal(int N){    float n = (float) ((5 + Math.sqrt(40 * N -                                      15)) / 10);     // Condition to check if N is a    // centered pentagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void main(String[] args){         // Given Number    int N = 6;     // Function call    if (isCenteredpentagonal(N))    {        System.out.print("Yes");    }    else    {        System.out.print("No");    }}} // This code is contributed by sapnasingh4991

## Python3

 # Python3 program for the above approachimport numpy as np # Function to check if number N# is a centered pentagonal numberdef isCenteredpentagonal(N):     n = (5 + np.sqrt(40 * N - 15)) / 10     # Condition to check if N is a    # centered pentagonal number    return (n - int(n)) == 0 # Driver CodeN = 6 # Function callif (isCenteredpentagonal(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 number N// is a centered pentagonal numberstatic bool isCenteredpentagonal(int N){    float n = (float) ((5 + Math.Sqrt(40 * N -                                      15)) / 10);     // Condition to check if N is a    // centered pentagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void Main(string[] args){         // Given number    int N = 6;     // Function call    if (isCenteredpentagonal(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)

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