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Code Number

Pentagonal number

In number theory, a pentagonal number is a figurate number that can be represented in the form of a regular pentagon. These numbers are obtained by counting the dots in the successive layers of a regular pentagon. The formula to calculate the nth pentagonal number is given by:

Pn = (3n^2 - n) / 2

Problem Statement

The task at hand is to write a program that calculates and prints the first 'k' pentagonal numbers, where 'k' is a given positive integer. The program should use the above formula to calculate each pentagonal number and then display the result.

Explanation with Suitable Example

Let's take an example with k = 6. The program should calculate and display the first 6 pentagonal numbers.

Pseudocode

function pentagonalNo(k)
    // Input: k - number of pentagonal numbers to be calculated

    for n = 1 to k do
        // Calculate the nth pentagonal number using the formula
        result = (3 * n^2 - n) / 2

        // Display the calculated pentagonal number
        print result

end function

Before diving into the code explanation, let's outline the pseudocode for the given task:

  1. Create a function pentagonalNo(k) to calculate and display the first 'k' pentagonal numbers.
  2. Inside the function, use a loop to iterate from n = 1 to n = k.
  3. For each 'n', calculate the pentagonal number using the formula: result = (3 * (n * n) - n) / 2.
  4. Print the calculated pentagonal number for each value of 'n'.

Code Solution

Here given code implementation process.

// C Program for
// Pentagonal number
#include <stdio.h>

void pentagonalNo(int k)
{
	// Print all initial k pentagonal number
	for (int n = 1; n <= k; ++n)
	{
		// Formula
		//  (3n²-n)
		//  —————————
		//     2
      
		// Calculate nth pentagonal number
		int result = (3 *(n *n) - n) / 2;
      
		// Display calculated result
		printf("  %d", result);
	}
}
int main()
{
	//  Pentagonal number are
	// —————————————————————————————————————————————
	//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
	//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
	//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
  
	// k = 10
	pentagonalNo(10);
	return 0;
}

Output

  1  5  12  22  35  51  70  92  117  145
// Java program for
// Pentagonal number
public class PentagonalNumber
{
	public void pentagonalNo(int k)
	{
		// Print all initial k pentagonal number
		for (int n = 1; n <= k; ++n)
		{
			// Formula
			//  (3n²-n)
			//  —————————
			//     2
          
			// Calculate nth pentagonal number
			int result = (3 * (n * n) - n) / 2;
          
			// Display calculated result
			System.out.print(" " + result);
		}
	}
	public static void main(String[] args)
	{
		PentagonalNumber task = new PentagonalNumber();
      
		//  Pentagonal number are
		// —————————————————————————————————————————————
		//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
		//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
		//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
		//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
		//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
      
		// k = 10
		task.pentagonalNo(10);
	}
}

Output

 1 5 12 22 35 51 70 92 117 145
// Include header file
#include <iostream>
using namespace std;

// C++ program for
// Pentagonal number

class PentagonalNumber
{
	public: void pentagonalNo(int k)
	{
		// Print all initial k pentagonal number
		for (int n = 1; n <= k; ++n)
		{
			// Formula
			//  (3n²-n)
			//  —————————
			//     2
          
			// Calculate nth pentagonal number
			int result = (3 *(n *n) - n) / 2;
          
			// Display calculated result
			cout << " " << result;
		}
	}
};
int main()
{
	PentagonalNumber *task = new PentagonalNumber();
	//  Pentagonal number are
	// —————————————————————————————————————————————
	//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
	//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
	//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
  
	// k = 10
	task->pentagonalNo(10);
	return 0;
}

Output

 1 5 12 22 35 51 70 92 117 145
// Include namespace system
using System;
// Csharp program for
// Pentagonal number
public class PentagonalNumber
{
	public void pentagonalNo(int k)
	{
		// Print all initial k pentagonal number
		for (int n = 1; n <= k; ++n)
		{
			// Formula
			//  (3n²-n)
			//  —————————
			//     2
          
			// Calculate nth pentagonal number
			int result = (3 * (n * n) - n) / 2;
          
			// Display calculated result
			Console.Write(" " + result);
		}
	}
	public static void Main(String[] args)
	{
		PentagonalNumber task = new PentagonalNumber();
		//  Pentagonal number are
		// —————————————————————————————————————————————
		//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
		//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
		//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
		//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
		//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
      
		// k = 10
		task.pentagonalNo(10);
	}
}

Output

 1 5 12 22 35 51 70 92 117 145
package main
import "fmt"
// Go program for
// Pentagonal number

func pentagonalNo(k int) {
	// Print all initial k pentagonal number
	for n := 1 ; n <= k ; n++ {
		// Formula
		//  (3n²-n)
		//  —————————
		//     2

		// Calculate nth pentagonal number
		var result int = (3 * (n * n) - n) / 2
		
		// Display calculated result
		fmt.Print(" ", result)
	}
}
func main() {

	//  Pentagonal number are
	// —————————————————————————————————————————————
	//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
	//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
	//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.

	// k = 10
	pentagonalNo(10)
}

Output

 1 5 12 22 35 51 70 92 117 145
<?php
// Php program for
// Pentagonal number
class PentagonalNumber
{
	public	function pentagonalNo($k)
	{
		// Print all initial k pentagonal number
		for ($n = 1; $n <= $k; ++$n)
		{
			// Formula
			//  (3n²-n)
			//  —————————
			//     2
          
			// Calculate nth pentagonal number
			$result = (int)((3 * ($n * $n) - $n) / 2);
          
			// Display calculated result
			echo(" ".$result);
		}
	}
}

function main()
{
	$task = new PentagonalNumber();
	//  Pentagonal number are
	// —————————————————————————————————————————————
	//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
	//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
	//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
  
	// k = 10
	$task->pentagonalNo(10);
}
main();

Output

 1 5 12 22 35 51 70 92 117 145
// Node JS program for
// Pentagonal number
class PentagonalNumber
{
	pentagonalNo(k)
	{
		// Print all initial k pentagonal number
		for (var n = 1; n <= k; ++n)
		{
			// Formula
			//  (3n²-n)
			//  —————————
			//     2
          
			// Calculate nth pentagonal number
			var result = parseInt((3 * (n * n) - n) / 2);
          
			// Display calculated result
			process.stdout.write(" " + result);
		}
	}
}

function main()
{
	var task = new PentagonalNumber();
	//  Pentagonal number are
	// —————————————————————————————————————————————
	//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
	//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
	//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
	// k = 10
	task.pentagonalNo(10);
}
main();

Output

 1 5 12 22 35 51 70 92 117 145
#  Python 3 program for
#  Pentagonal number
class PentagonalNumber :
	def pentagonalNo(self, k) :
		n = 1
		#  Print all initial k pentagonal number
		while (n <= k) :
			#  Formula
			#   (3n²-n)
			#   —————————
			#      2
            
			#  Calculate nth pentagonal number
			result = int((3 * (n * n) - n) / 2)

			#  Display calculated result
			print(" ", result, end = "")
			n += 1
		
	

def main() :
	task = PentagonalNumber()
	#   Pentagonal number are
	#  —————————————————————————————————————————————
	#   1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	#   210, 247, 287, 330, 376, 425, 477, 532, 590, 
	#   651, 715, 782, 852, 925, 1001, 1080, 1162, 
	#   1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	#   2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
    
	#  k = 10
	task.pentagonalNo(10)

if __name__ == "__main__": main()

Output

  1  5  12  22  35  51  70  92  117  145
#  Ruby program for
#  Pentagonal number
class PentagonalNumber 
	def pentagonalNo(k) 
		n = 1
		#  Print all initial k pentagonal number
		while (n <= k) 
			#  Formula
			#   (3n²-n)
			#   —————————
			#      2
            
			#  Calculate nth pentagonal number
			result = (3 * (n * n) - n) / 2

			#  Display calculated result
			print(" ", result)
			n += 1
		end

	end

end

def main() 
	task = PentagonalNumber.new()
	#   Pentagonal number are
	#  —————————————————————————————————————————————
	#   1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	#   210, 247, 287, 330, 376, 425, 477, 532, 590, 
	#   651, 715, 782, 852, 925, 1001, 1080, 1162, 
	#   1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	#   2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
    
	#  k = 10
	task.pentagonalNo(10)
end

main()

Output

 1 5 12 22 35 51 70 92 117 145
// Scala program for
// Pentagonal number
class PentagonalNumber()
{
	def pentagonalNo(k: Int): Unit = {
		var n: Int = 1;
		// Print all initial k pentagonal number
		while (n <= k)
		{
			// Formula
			//  (3n²-n)
			//  —————————
			//     2
          
			// Calculate nth pentagonal number
			var result: Int = (3 * (n * n) - n) / 2;
          
			// Display calculated result
			print(" " + result);
			n += 1;
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: PentagonalNumber = new PentagonalNumber();
		//  Pentagonal number are
		// —————————————————————————————————————————————
		//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
		//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
		//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
		//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
		//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
  
		// k = 10
		task.pentagonalNo(10);
	}
}

Output

 1 5 12 22 35 51 70 92 117 145
// Swift 4 program for
// Pentagonal number
class PentagonalNumber
{
	func pentagonalNo(_ k: Int)
	{
		var n: Int = 1;
		// Print all initial k pentagonal number
		while (n <= k)
		{
			// Formula
			//  (3n²-n)
			//  —————————
			//     2
          
			// Calculate nth pentagonal number
			let result: Int = (3 * (n * n) - n) / 2;
          
			// Display calculated result
			print(" ", result, terminator: "");
			n += 1;
		}
	}
}
func main()
{
	let task: PentagonalNumber = PentagonalNumber();
	//  Pentagonal number are
	// —————————————————————————————————————————————
	//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
	//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
	//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
  
	// k = 10
	task.pentagonalNo(10);
}
main();

Output

  1  5  12  22  35  51  70  92  117  145
// Kotlin program for
// Pentagonal number
class PentagonalNumber
{
	fun pentagonalNo(k: Int): Unit
	{
		var n: Int = 1;
		// Print all initial k pentagonal number
		while (n <= k)
		{
			// Formula
			//  (3n²-n)
			//  —————————
			//     2
          
			// Calculate nth pentagonal number
			val result: Int = (3 * (n * n) - n) / 2;
          
			// Display calculated result
			print(" " + result);
			n += 1;
		}
	}
}
fun main(args: Array < String > ): Unit
{
	val task: PentagonalNumber = PentagonalNumber();
	//  Pentagonal number are
	// —————————————————————————————————————————————
	//  1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 
	//  210, 247, 287, 330, 376, 425, 477, 532, 590, 
	//  651, 715, 782, 852, 925, 1001, 1080, 1162, 
	//  1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 
	//  2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882 etc.
  
	// k = 10
	task.pentagonalNo(10);
}

Output

 1 5 12 22 35 51 70 92 117 145

Output Explanation

The program is executed with 'k' as 10, so it will calculate the first 10 pentagonal numbers and print the results. The output will be:

1  5  12  22  35  51  70  92  117  145

Each number in the output represents the first 10 pentagonal numbers.

Time Complexity Analysis

In the given program, the function pentagonalNo(k) runs a loop from 1 to 'k' to calculate 'k' pentagonal numbers. For each value of 'n', the calculation involves basic arithmetic operations, which can be considered constant time operations.

Therefore, the time complexity of the program is O(k), where 'k' is the number of pentagonal numbers to be calculated.

Finally

In this program, we have successfully calculated the first 'k' pentagonal numbers using the given formula. We've explained the code step by step, provided suitable examples, and outlined the time complexity. Pentagonal numbers have applications in various areas, including number theory, geometry, and combinatorics. The program can be extended or used as a part of a larger application where pentagonal numbers are required.

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