Moran Numbers in Java

In this tutorial, we will be discussing Moran numbers in Java. A moran number is a number, when divided by the sum of its digits, generates a prime number. Note that the sum of the digits of the number should be the factor of that number. Let's understand with the help of a few examples.

Example 1:

Input: 45

Output: 45 is a Moran number.

Explanation: The sum of the digits of the number 45 is 4 + 5 = 9, and when 45 is divided by 9, we get 45 / 9 = 5, and 5 is a prime number. Hence, 45 is a Moran number.

Example 2:

Input: 36

Output: 36 is not a Moran number.

Explanation: The sum of the digits of the number 36 is 3 + 6 = 9, and when 36 is divided by 9, we get 36 / 9 = 4, and 4 is not a prime number. Hence, 36 is not a Moran number.

Example 3:

Input: 22

Output: 22 is not a Moran number.

Explanation: The sum of the digits of the number 22 is 2 + 2 = 4, and 4 is not the factor of the number 22. Hence, 22 is not a Moran number.

Validation For the Moran Number

Observe the following algorithm.

Step 1: Take a number n.

Step 2: Compute the sum of the digits of the number n.

Step 3: Check whether the sum of the digits is the factor of the number n or not.

If the sum of the digit is not the factor, we can say that the number n is not the Moran number.
If the sum of the digit is the factor, then we check whether the answer that comes after dividing the number by the digits sum of the number is a prime number or not.
If the number that comes after the division is a prime number, then the given input number is a Moran number; otherwise, not.

Implementation

Observe the implementation of the above algorithm.

FileName: MoranNum.java

public class MoranNum 
{

// a method that computes the sum of the digits of the number
// num
public int findSumDigits(int num)
{
    int sum = 0;
    
    while(num != 0)
    {
        sum = sum + (num % 10);
        num = num / 10;
    }
    
    return sum;
}

// a method that checks whether the number num
// is a prime number or not
public boolean isPrime(int num)
{
    for(int i = 2; i <= (int)Math.sqrt(num); i++)
    {
        if((num % i) == 0)
        {
            return false;
        }
    }
    
    return true;
}

// a method that returns true if the number n
// is a moran number
public boolean isMoran(int n) 
{
    int sumDig = findSumDigits(n);
    
    // if number n is not completely divided by the 
    // sumDig, then n can never be a moran number
    if((n % sumDig) != 0)
    {
        return false;
    }
    
    // reaching here means sumDig a factor of
    // the number n. Now we find the quotient or 
    // or answer of the division
    int div = n / sumDig;
    
    // if the answer of the division is a prime
    // number, then n is a moran number; 
    if(isPrime(div))
    {
        return true;
    }

    // reaching here means div is not a prime number
    // hence, n is not a moran number
    return false;
}
    
// main method
public static void main(String[] argvs)
{
// creating an object of the class MoranNum
MoranNum obj = new MoranNum();

// input 1
int num = 45;

boolean ans = obj.isMoran(num);

if(ans)
{
    System.out.println("The number " + num + " is a Moran number.");
}
else
{
    System.out.println("The number " + num + " is not a Moran number.");    
}

System.out.println();

// input 2
num = 36;

ans = obj.isMoran(num);

if(ans)
{
    System.out.println("The number " + num + " is a Moran number.");
}
else
{
    System.out.println("The number " + num + " is not a Moran number.");    
}

System.out.println();

// input 3
num = 22;

ans = obj.isMoran(num);

if(ans)
{
    System.out.println("The number " + num + " is a Moran number.");
}
else
{
    System.out.println("The number " + num + " is not a Moran number.");    
}

}
}

Output:

The number 45 is a Moran number.

The number 36 is not a Moran number.

The number 22 is not a Moran number.

Finding Moran Numbers Within A Range

In this approach, we will be using a sieve to find the moran numbers within the given range. We are using the sieve because we do not want to use a loop for doing the validation for a prime number. The rest of the other stuff remains the same as the above-written approach. Observe the program.

FileName: MoranNum1.java

// import statement for the ArrrayList
import java.util.ArrayList;

public class MoranNum1
{
public boolean primeArr[];

// constructor of the class
public MoranNum1(int num)
{
    // creating a boolean array
    // initially all the values the boolean array is false
    primeArr = new boolean[num + 1];
    
}
// a method that computes the sum of the digits of the number
// num
public int findSumDigits(int num)
{
    int sum = 0;
    
    while(num != 0)
    {
        sum = sum + (num % 10);
        num = num / 10;
    }
    
    return sum;
}

// a method that checks whether the number num
// is a prime number or not
public void findPrime(int num)
{
    // computing the size of the primeArr array
    int size = primeArr.length;
    
    // starting the loop from 2
    // because 0 and 1 are not prime numbers
    for(int i = 2; i < size; i++)
    {
        primeArr[i] = true;
    }
    
        // filtering out prime numbers using the 
        // Sieve of Eratosthenes technique
        for(int i = 2 ; i < size; i++)
        {
            primeArr[i] = true;
        }
        
        
        for(int i = 2; (i * i) <= num; i++)
        {
            if(primeArr[i])
            {
                // multiple of a prime number can never be a prime number
                for(int j = i * i; j <= num; j = j + i)
                {
                    primeArr[j] = false;
                }
            }
        }

}

// a method that retuns all the moran numbers
// that lies within the range 1 to n
public ArrayList<Integer> findMoran(int n) 
{
    ArrayList<Integer> al = new ArrayList<Integer>();
    for(int i = 1; i <= n; i++)
    {
        int sumDig = findSumDigits(i);
        
        // if number i is not completely divided by the 
        // sumDig, then i can never be a Moran number
        if((i % sumDig) != 0)
        {
            continue;
        }
        
        // reaching here means sumDig a factor of
        // the number i. Now we find the quotient or 
        // or answer of the division
        int div = i / sumDig;
        
        // if the answer of the division is a prime
        // number, then i is a Moran number. Hence,
        // it can be added into the list
        if(primeArr[div])
        {
            al.add(i);
        }
    
    }
    
    return al;
}
    
// main method
public static void main(String[] argvs)
{
// we will find the Moran number lying within the range 1 to 200
int range = 200;
// creating an object of the class MoranNum1
MoranNum1 obj = new MoranNum1(range);
obj.findPrime(range);

ArrayList<Integer> res = obj.findMoran(range);

System.out.println("The Moran numbers that lie within the range 1 to " + range + " are: ");

int size = res.size();

for(int i = 0; i < size; i++)
{
    System.out.print(res.get(i) + " ");
}


}
}

Output:

The Moran numbers that lie within the range 1 to 200 are: 
18 21 27 42 45 63 84 111 114 117 133 152 153 156 171 190 195 198

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