Given an integer **N**, the task is to check if it is a Centered heptagonal number or not.

Centered heptagonal numberis centered figure number that represents a heptagon with dot in center and all other dot surrounding in heptagonal form..The first few Centered heptagonal number are 1, 8, 22, 43, 71, 106, 148, …

**Examples:**

Input:N = 8Output:YesExplanation:

8 is the Second Centered heptagonal number.Input:20Output:NoExplanation:

20 is not a Centered heptagonal number.

**Approach:**

To solve the problem mentioned above we have to know that the K^{th} term of the Centered heptagonal number is given as:

As we have to check that the given number can be expressed as a Centered heptagonal number or not. This can be checked by generalizing the equation as:

=>

=>

Finally, check the value of computation using this formula if it is an integer, if yes then it means that N is a Centered heptagonal number.

Below is the implementation of the above approach:

## C++

`// C++ implementation to check that` `// a number is a Centered` `// heptagonal number or not` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check that the` `// number is a Centered` `// heptagonal number` `bool` `isCenteredheptagonal(` `int` `N)` `{` ` ` `float` `n = (7 + ` `sqrt` `(56 * N - 7)) / 14;` ` ` `// Condition to check if the` ` ` `// number is a Centered heptagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 8;` ` ` `// Function call` ` ` `if` `(isCenteredheptagonal(n)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java implementation to check that` `// a number is a Centered` `// heptagonal number or not` `import` `java.lang.Math;` `class` `GFG` `{` ` ` `// Function to check that the` `// number is a Centered` `// heptagonal number` `public` `static` `boolean` `isCenteredheptagonal(` `int` `N)` `{` ` ` `double` `n = (` `7` `+ Math.sqrt(` `56` `* N - ` `7` `)) / ` `14` `;` ` ` `// Condition to check if the` ` ` `// number is a Centered heptagonal number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `8` `;` ` ` `// Function call` ` ` `if` `(isCenteredheptagonal(n))` ` ` `{` ` ` `System.out.println(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.println(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by divyeshrabadiya07` |

## Python3

`# Python3 implementation to check` `# that a number is a centered` `# heptagonal number or not` `import` `math` `# Function to check that the` `# number is a centered` `# heptagonal number` `def` `isCenteredheptagonal(N):` ` ` ` ` `n ` `=` `(` `7` `+` `math.sqrt(` `56` `*` `N ` `-` `7` `)) ` `/` `14` ` ` ` ` `# Condition to check if the number` ` ` `# is a centered heptagonal number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` ` ` `# Driver Code` `n ` `=` `8` `# Function call` `if` `(isCenteredheptagonal(n)):` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` ` ` `# This code is contributed by ShubhamCoder` |

## C#

`// C# implementation to check that` `// a number is a centered` `// heptagonal number or not` `using` `System;` `class` `GFG{` `// Function to check that the` `// number is a centered` `// heptagonal number` `static` `bool` `isCenteredheptagonal(` `int` `N)` `{` ` ` `double` `n = (7 + Math.Sqrt(56 * N - 7)) / 14;` ` ` ` ` `// Condition to check if the number` ` ` `// is a centered heptagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` ` ` `// Driver Code` `static` `public` `void` `Main ()` `{` ` ` `int` `n = 8;` ` ` ` ` `// Function call` ` ` `if` `(isCenteredheptagonal(n))` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by ShubhamCoder` |

## Javascript

`<script>` `// Javascript implementation to check that` `// a number is a Centered` `// heptagonal number or not` `// Function to check that the` `// number is a Centered` `// heptagonal number` `function` `isCenteredheptagonal(N)` `{` ` ` `let n = (7 + Math.sqrt(56 * N - 7)) / 14;` ` ` `// Condition to check if the` ` ` `// number is a Centered heptagonal number` ` ` `return` `(n - parseInt(n)) == 0;` `}` `// Driver Code` `let n = 8;` `// Function call` `if` `(isCenteredheptagonal(n)) {` ` ` `document.write(` `"Yes"` `);` `}` `else` `{` ` ` `document.write(` `"No"` `);` `}` `// This code is contributed by rishavmahato348.` `</script>` |

**Output:**

Yes

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