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Code Number

Find Nth Kynea Number

A Kynea number, also known as a Kynea Mersenne number, is a special type of number that can be expressed as (2^(2 * n)) + (2^n) - 1, where 'n' is a non-negative integer. In mathematical terms, the nth Kynea number is defined as Kn = (2^(2 * n)) + (2^n) - 1.

Problem Statement

The task is to find the nth Kynea number for a given non-negative integer 'n' using the formula mentioned above.

Explanation with Suitable Example

Let's understand the process of finding the Kynea numbers with an example for n = 4.

  • We need to find the 4th Kynea number, so we put n = 4 in the formula: K4 = (2^(2 * 4)) + (2^4) - 1
  • Calculate the values: K4 = (2^8) + (2^4) - 1 = 256 + 16 - 1 = 271.
  • Therefore, the 4th Kynea number is 271.

Pseudocode and Algorithm

  1. Create a function findPower that takes two integers number and size as input and returns an integer.

    • If number is 0, return 0.
    • If size is 0, return 1.
    • Initialize a variable result to number.
    • Run a loop from 2 to size (inclusive) and update result by multiplying it with number in each iteration.
    • Return result.

  2. Create a function nthKyneaNo that takes an integer number as input and does not return anything.

    • If number is less than or equal to 0, return (no valid Kynea number for negative or zero 'n').
    • Calculate the 2^(2 * number) using findPower(2, 2 * number).
    • Calculate the 2^(number + 1) using findPower(2, number + 1).
    • Subtract 1 from the sum of the above two calculated values.
    • Print the output as number + " 'nth Kynea number is : " + result.

Code Solution

Here given code implementation process.

/*
  Java Program for
  Find Nth Kynea Number
*/
public class KyneaNumber
{
    public int findPower(int number, int size)
    {
        if (number == 0)
        {
            return 0;
        }
        else if (size == 0)
        {
            return 1;
        }
        else
        {
            int result = number;
            for (int i = 2; i <= size; ++i)
            {
                result = result * number;
            }
            return result;
        }
    }
    public void nthKyneaNo(int number)
    {
        if (number <= 0)
        {
            // When invalid kynea number
            return;
        }
        int result = (findPower(2, 2 * number) + findPower(2, number + 1) - 1);
        System.out.println(number + " 'nth Kynea number is : " + result);
    }
    public static void main(String[] args)
    {
        KyneaNumber task = new KyneaNumber();
        // Test Case
        task.nthKyneaNo(4);
        task.nthKyneaNo(7);
        task.nthKyneaNo(9);
        task.nthKyneaNo(15);
    }
}

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
// Include namespace system
using System;
/*
  Csharp Program for
  Find Nth Kynea Number
*/
public class KyneaNumber
{
    public int findPower(int number, int size)
    {
        if (number == 0)
        {
            return 0;
        }
        else if (size == 0)
        {
            return 1;
        }
        else
        {
            var result = number;
            for (var i = 2; i <= size; ++i)
            {
                result = result * number;
            }
            return result;
        }
    }
    public void nthKyneaNo(int number)
    {
        if (number <= 0)
        {
            // When invalid kynea number
            return;
        }
        var result = (this.findPower(2, 2 * number) + 
                      this.findPower(2, number + 1) - 1);
        Console.WriteLine(number + " 'nth Kynea number is : " +
                          result);
    }
    public static void Main(String[] args)
    {
        var task = new KyneaNumber();
        // Test Case
        task.nthKyneaNo(4);
        task.nthKyneaNo(7);
        task.nthKyneaNo(9);
        task.nthKyneaNo(15);
    }
}

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
// Include header file
#include <iostream>
using namespace std;
/*
  C++ Program for
  Find Nth Kynea Number
*/
class KyneaNumber
{
    public: int findPower(int number, int size)
    {
        if (number == 0)
        {
            return 0;
        }
        else if (size == 0)
        {
            return 1;
        }
        else
        {
            int result = number;
            for (int i = 2; i <= size; ++i)
            {
                result = result *number;
            }
            return result;
        }
    }
    void nthKyneaNo(int number)
    {
        if (number <= 0)
        {
            // When invalid kynea number
            return;
        }
        int result = (this->findPower(2, 2 *number) + 
                      this->findPower(2, number + 1) - 1);
        cout << number << " \'nth Kynea number is : " << result << endl;
    }
};
int main()
{
    KyneaNumber *task = new KyneaNumber();
    // Test Case
    task->nthKyneaNo(4);
    task->nthKyneaNo(7);
    task->nthKyneaNo(9);
    task->nthKyneaNo(15);
    return 0;
}

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
// C Program for
// Find Nth Kynea Number
#include <stdio.h>

int pow_number(int number, int size)
{
    if (number == 0)
    {
        return 0;
    }
    else if (size == 0)
    {
        return 1;
    }
    else
    {
        int result = number;
        for (int i = 2; i <= size; ++i)
        {
            result = result *number;
        }
        return result;
    }
}
void kynea_number(int number)
{
    if (number <= 0)
    {
        // When invalid kynea number
        return;
    }
    printf("%d 'nth Kynea number is : %d\n", number, 
           (pow_number(2, 2 *number) + pow_number(2, number + 1) - 1));
}
int main()
{
    kynea_number(4);
    kynea_number(7);
    kynea_number(9);
    kynea_number(15);
    return 0;
}

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
package main
import "fmt"
/*
  Go Program for
  Find Nth Kynea Number
*/

func findPower(number, size int) int {
    if number == 0 {
        return 0
    } else if size == 0 {
        return 1
    } else {
        var result int = number
        for i := 2 ; i <= size ; i++ {
            result = result * number
        }
        return result
    }
}
func nthKyneaNo(number int) {
    if number <= 0 {
        // When invalid kynea number
        return
    }
    var result int = (findPower(2, 2 * number) + findPower(2, number + 1) - 1)
    fmt.Println(number, "'nth Kynea number is :", result)
}
func main() {
    
    // Test Case
    nthKyneaNo(4)
    nthKyneaNo(7)
    nthKyneaNo(9)
    nthKyneaNo(15)
}

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
<?php
/*
  Php Program for
  Find Nth Kynea Number
*/
class KyneaNumber
{
    public  function findPower($number, $size)
    {
        if ($number == 0)
        {
            return 0;
        }
        else if ($size == 0)
        {
            return 1;
        }
        else
        {
            $result = $number;
            for ($i = 2; $i <= $size; ++$i)
            {
                $result = $result * $number;
            }
            return $result;
        }
    }
    public  function nthKyneaNo($number)
    {
        if ($number <= 0)
        {
            // When invalid kynea number
            return;
        }
        $result = ($this->findPower(2, 2 * $number) + 
                   $this->findPower(2, $number + 1) - 1);
        printf("%s\n", $number.
            " 'nth Kynea number is : ".strval($result));
    }
    public static
    function main($args)
    {
        $task = new KyneaNumber();
        // Test Case
        $task->nthKyneaNo(4);
        $task->nthKyneaNo(7);
        $task->nthKyneaNo(9);
        $task->nthKyneaNo(15);
    }
}
KyneaNumber::main(array());

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
/*
  Node JS Program for
  Find Nth Kynea Number
*/
class KyneaNumber
{
    findPower(number, size)
    {
        if (number == 0)
        {
            return 0;
        }
        else if (size == 0)
        {
            return 1;
        }
        else
        {
            var result = number;
            for (var i = 2; i <= size; ++i)
            {
                result = result * number;
            }
            return result;
        }
    }
    nthKyneaNo(number)
    {
        if (number <= 0)
        {
            // When invalid kynea number
            return;
        }
        var result = (this.findPower(2, 2 * number) + 
                      this.findPower(2, number + 1) - 1);
        console.log(number + " 'nth Kynea number is : " + result);
    }
}

function main()
{
    var task = new KyneaNumber();
    // Test Case
    task.nthKyneaNo(4);
    task.nthKyneaNo(7);
    task.nthKyneaNo(9);
    task.nthKyneaNo(15);
}
// Start program execution
main();

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
#  Python 3 Program for
#  Find Nth Kynea Number
class KyneaNumber :
    def findPower(self, number, size) :
        if (number == 0) :
            return 0
        elif (size == 0) :
            return 1
        else :
            result = number
            i = 2
            while (i <= size) :
                result = result * number
                i += 1
            
            return result
        
    
    def nthKyneaNo(self, number) :
        if (number <= 0) :
            #  When invalid kynea number
            return
        
        result = (self.findPower(2, 2 * number) + 
                  self.findPower(2, number + 1) - 1)
        print(number ,"'nth Kynea number is :", result)
    

def main() :
    task = KyneaNumber()
    #  Test Case
    task.nthKyneaNo(4)
    task.nthKyneaNo(7)
    task.nthKyneaNo(9)
    task.nthKyneaNo(15)

if __name__ == "__main__": main()

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
#  Ruby Program for
#  Find Nth Kynea Number
class KyneaNumber 
    def findPower(number, size) 
        if (number == 0) 
            return 0
        elsif (size == 0) 
            return 1
        else
 
            result = number
            i = 2
            while (i <= size) 
                result = result * number
                i += 1
            end

            return result
        end

    end

    def nthKyneaNo(number) 
        if (number <= 0) 
            #  When invalid kynea number
            return
        end

        result = (self.findPower(2, 2 * number) + 
                  self.findPower(2, number + 1) - 1)
        print(number ,"'nth Kynea number is : ", result, "\n")
    end

end

def main() 
    task = KyneaNumber.new()
    #  Test Case
    task.nthKyneaNo(4)
    task.nthKyneaNo(7)
    task.nthKyneaNo(9)
    task.nthKyneaNo(15)
end

main()

Output

4'nth Kynea number is : 287
7'nth Kynea number is : 16639
9'nth Kynea number is : 263167
15'nth Kynea number is : 1073807359

/*
  Scala Program for
  Find Nth Kynea Number
*/
class KyneaNumber()
{
    def findPower(number: Int, size: Int): Int = {
        if (number == 0)
        {
            return 0;
        }
        else if (size == 0)
        {
            return 1;
        }
        else
        {
            var result: Int = number;
            var i: Int = 2;
            while (i <= size)
            {
                result = result * number;
                i += 1;
            }
            return result;
        }
    }
    def nthKyneaNo(number: Int): Unit = {
        if (number <= 0)
        {
            // When invalid kynea number
            return;
        }
        var result: Int = (findPower(2, 2 * number) + 
          findPower(2, number + 1) - 1);
        println(""+ number + " 'nth Kynea number is : " + result);
    }
}
object Main
{
    def main(args: Array[String]): Unit = {
        var task: KyneaNumber = new KyneaNumber();
        // Test Case
        task.nthKyneaNo(4);
        task.nthKyneaNo(7);
        task.nthKyneaNo(9);
        task.nthKyneaNo(15);
    }
}

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
import Foundation
/*
  Swift 4 Program for
  Find Nth Kynea Number
*/
class KyneaNumber
{
    func findPower(_ number: Int, _ size: Int) -> Int
    {
        if (number == 0)
        {
            return 0;
        }
        else if (size == 0)
        {
            return 1;
        }
        else
        {
            var result: Int = number;
            var i: Int = 2;
            while (i <= size)
            {
                result = result * number;
                i += 1;
            }
            return result;
        }
    }
    func nthKyneaNo(_ number: Int)
    {
        if (number <= 0)
        {
            // When invalid kynea number
            return;
        }
        let result: Int = (self.findPower(2, 2 * number) + 
                           self.findPower(2, number + 1) - 1);
        print(String(number) + " \'nth Kynea number is : " + String(result));
    }
    static func main(_ args: [String])
    {
        let task: KyneaNumber? = KyneaNumber();
        // Test Case
        task!.nthKyneaNo(4);
        task!.nthKyneaNo(7);
        task!.nthKyneaNo(9);
        task!.nthKyneaNo(15);
    }
}
KyneaNumber.main([String]());

Output

4 'nth Kynea number is : 287
7 'nth Kynea number is : 16639
9 'nth Kynea number is : 263167
15 'nth Kynea number is : 1073807359
/*
  Kotlin Program for
  Find Nth Kynea Number
*/
class KyneaNumber
{
    fun findPower(number: Int, size: Int): Int
    {
        if (number == 0)
        {
            return 0;
        }
        else if (size == 0)
        {
            return 1;
        }
        else
        {
            var result: Int = number;
            var i: Int = 2;
            while (i <= size)
            {
                result = result * number;
                i += 1;
            }
            return result;
        }
    }
    fun nthKyneaNo(number: Int): Unit
    {
        if (number <= 0)
        {
            // When invalid kynea number
            return;
        }
        val result: Int = (this.findPower(2, 2 * number) + 
                           this.findPower(2, number + 1) - 1);
        println(""+number + "'nth Kynea number is : " + result);
    }
}
fun main(args: Array < String > ): Unit
{
    val task: KyneaNumber = KyneaNumber();
    // Test Case
    task.nthKyneaNo(4);
    task.nthKyneaNo(7);
    task.nthKyneaNo(9);
    task.nthKyneaNo(15);
}

Output

4'nth Kynea number is : 287
7'nth Kynea number is : 16639
9'nth Kynea number is : 263167
15'nth Kynea number is : 1073807359

Java Code Explanation

The provided Java code follows the algorithm described above.

  1. The findPower function computes the power of a number using a loop.
  2. The nthKyneaNo function calculates the Kynea number using the provided formula and prints the result.

Output Explanation

The given Java code has been tested with four test cases: 4, 7, 9, and 15.

  • For n = 4, the 4th Kynea number is calculated as 271.
  • For n = 7, the 7th Kynea number is calculated as 16639.
  • For n = 9, the 9th Kynea number is calculated as 263167.
  • For n = 15, the 15th Kynea number is calculated as 1073807359.

Time Complexity

  1. The findPower function runs a loop 'size' times, so its time complexity is O(size).
  2. The nthKyneaNo function involves calling findPower twice, so its time complexity can be considered as O(size).

It is important to note that the value of 'size' is proportional to the value of 'n'. So, the time complexity can be represented as O(n).

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