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### CodeVita 2013 : Solution of Game of Primes

The problem statement is as given below :

Problem
In a global Mathematics contest, the contestants are told to invent some special numbers which can be built by adding the squares of its digits. Doing this perpetually, the numbers will end up to 1 or 4.
If a positive integer ends with 1, then it is called the Number of Game.
An example from above is:
13 = 1^2 + 3^2 = 1+9 = 10 (Step:1)
10 = 1^2 + 0^2 = 1+0 = 1 (Step:2), iteration ends in Step 2 since number ends with 1

Then in next round, the contestants are asked to combine their newly invented number, i.e. Number of Game with prime number.
Now, being a smart programmer, write a program to help the contestants to find out the Nth combined number within any given range, where N can be any integer.

Input Format:

Input consists of 3 integers X, Y, N, one on each line. X and Y are upper and lower limits of the range. The range is inclusive of both X and Y. Find Nth number in range [X,Y].

 Line 1 X,where X is the upper limit of the range Line 2 Y,where Y is the lower limit of the range Line 3 N,where Nth element of the series is required

Constraints:

X <= Y
X > 0
N > 0

Output Format:

Output will show the Nth element of the combined series lying in the range between X and Y.

 Line 1 For Valid Input,print U,where U is the Nth element of the combined number series lying in the range between X and Y. Or No number is present at this index For Invalid Input,print Invalid Input

Sample Input and Output

SNo.InputOutput
1
1
30
3
19
2
12
33
5
No number is present at this index
3
-5
@
4
Invalid Input

Solution :

```import java.util.Scanner;

/**
*
* @author VIK
*/
public class GameOfPrimes {

public static void main(String[] args) {
Scanner sc=new Scanner(System.in);
try{

int lower=0,upper=0,n=0;
boolean flag=false;
try {
lower=Integer.parseInt(sc.nextLine().trim());

} catch (Exception e) {
flag=true;
}
try {
upper =Integer.parseInt(sc.nextLine().trim());

} catch (Exception e) {
flag=true;
}
try {
n=Integer.parseInt(sc.nextLine().trim());
} catch (Exception e) {
flag=true;
}
if(flag)
throw new Exception();
if(lower>upper || lower<=0 || n<=0)
throw new Exception();

int count=0;
int i=lower;
for (i = lower; i <=upper; i++) {
if(isPrime(i) && getJohn(i)==1)
{
count++;
// System.out.println(count+" "+i+" "+getJohn(i));
if(count==n)
{    System.out.println(i);
break;
}

}

}
if(i>upper)
{
System.out.println("No number is present at this index");
}
}catch(Exception e)
{
System.out.println("Invalid Input");
}
}

public static boolean isPrime(int num) {
boolean flag = false;
if (num < 2) {
return flag;
}
if (num == 2) {
return true;
}
if (num % 2 == 0) {
return flag;
}
int i = 3;
int rootn = (int) Math.sqrt(num);
for (; i <= rootn; i += 2) {
if (num % i == 0) {
break;
}

}
if (i > rootn) {
flag = true;
}
return flag;
}
static int getJohn(int y)
{
if(y<=4)
{
return y;
}
if(y==10)
return 1;
String s=y+"";

char[] c=s.trim().toCharArray();
int sum=0;
for (int i = 0; i < c.length; i++) {
sum+=Math.pow(Integer.parseInt(c[i]+"".trim()),2);
}

sum= getJohn(sum);
return sum;

}
}

```