# Program to check if N is a Tridecagonal Number or not

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

Tridecagon numberis a thirteen-sided polygon. The first few Tridecagon numbers are 1, 13, 36, 70, 115, 171, …

**Examples:**

Input:N = 13Output:YesExplanation:

Second Tridecagon number is 13.Input:N = 30Output:No

**Approach:**

- The K
^{th}term of the Tridecagon number is given as

- As we have to check that the given number can be expressed as a Tridecagon number or not. This can be checked as follows –

=>

=>

- Finally, check the value of computed using this formulae is an integer, which means that N is a Tridecagon number.

Below is the implementation of the above approach:

## C++

`// C++ implementation to check that` `// a number is a Tridecagon number or not` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check that the` `// number is a Tridecagon number` `bool` `isTridecagon(` `int` `N)` `{` ` ` `float` `n` ` ` `= (9 + ` `sqrt` `(88 * N + 81))` ` ` `/ 22;` ` ` `// Condition to check if the` ` ` `// number is a Tridecagon number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `i = 13;` ` ` `// Function call` ` ` `if` `(isTridecagon(i)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java implementation to check that a` `// number is a tridecagon number or not` `class` `GFG{` `// Function to check that the` `// number is a tridecagon number` `static` `boolean` `isTridecagon(` `int` `N)` `{` ` ` `float` `n = (` `float` `) ((` `9` `+ Math.sqrt(` `88` `* N +` ` ` `81` `)) / ` `22` `);` ` ` `// Condition to check if the` ` ` `// number is a tridecagon number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `i = ` `13` `;` ` ` `// Function call` ` ` `if` `(isTridecagon(i))` ` ` `{` ` ` `System.out.print(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.print(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by 29AjayKumar` |

## Python3

`# Python3 implementation to check that` `# a number is a tridecagon number or not` `import` `math` `# Function to check that the` `# number is a tridecagon number` `def` `isTridecagon(N):` ` ` `n ` `=` `(` `9` `+` `math.sqrt(` `88` `*` `N ` `+` `81` `)) ` `/` `22` ` ` `# Condition to check if the` ` ` `# number is a tridecagon number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` `# Driver Code` `i ` `=` `13` `# Function call` `if` `(isTridecagon(i)):` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` ` ` `# This code is contributed by divyamohan123` |

## C#

`// C# implementation to check that a` `// number is a tridecagon number or not` `using` `System;` `class` `GFG{` `// Function to check that the` `// number is a tridecagon number` `static` `bool` `isTridecagon(` `int` `N)` `{` ` ` `float` `n = (` `float` `)((9 + Math.Sqrt(88 * N +` ` ` `81)) / 22);` ` ` `// Condition to check if the` ` ` `// number is a tridecagon number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `public` `static` `void` `Main()` `{` ` ` `int` `i = 13;` ` ` `// Function call` ` ` `if` `(isTridecagon(i))` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by Code_Mech` |

## Javascript

`<script>` `// JavaScript implementation to check that` `// a number is a Tridecagon number or not` `// Function to check that the` `// number is a Tridecagon number` `function` `isTridecagon(N)` `{` ` ` `var` `n` ` ` `= (9 + Math.sqrt(88 * N + 81))` ` ` `/ 22;` ` ` `// Condition to check if the` ` ` `// number is a Tridecagon number` ` ` `return` `(n - parseInt(n)) == 0;` `}` `// Driver Code` `var` `i = 13;` `// Function call` `if` `(isTridecagon(i)) {` ` ` `document.write(` `"Yes"` `);` `}` `else` `{` ` ` `document.write(` `"No"` `);` `}` `</script>` |

**Output:**

Yes

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

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