Added Keith No. Program (Hacktoberfest2021) (#2342)

Co-authored-by: Andrii Siriak <siryaka@gmail.com>

Maths/KeithNumber.java

@@ -0,0 +1,50 @@
+import java.util.*;  
+class KeithNumber  
+{  
+    //user-defined function that checks if the given number is Keith or not  
+    static boolean isKeith(int x)  
+    {  
+        //List stores all the digits of the X  
+        ArrayList<Integer> terms=new ArrayList<Integer>();  
+        //n denotes the number of digits   
+        int temp = x, n = 0;   
+        //executes until the condition becomes false  
+        while (temp > 0)  
+        {  
+            //determines the last digit of the number and add it to the List      
+            terms.add(temp%10);  
+            //removes the last digit  
+            temp = temp/10;  
+            //increments the number of digits (n) by 1  
+            n++;  
+        }  
+        //reverse the List  
+        Collections.reverse(terms);  
+        int next_term = 0, i = n;  
+        //finds next term for the series  
+        //loop executes until the condition returns true  
+        while (next_term < x)  
+        {  
+            next_term = 0;  
+            //next term is the sum of previous n terms (it depends on number of digits the number has)  
+            for (int j=1; j<=n; j++)  
+            next_term = next_term + terms.get(i-j);  
+            terms.add(next_term);  
+            i++;  
+        }  
+        //when the control comes out of the while loop, there will be two conditions:  
+        //either next_term will be equal to x or greater than x  
+        //if equal, the given number is Keith, else not  
+        return (next_term == x);  
+    }  
+    //driver code  
+    public static void main(String[] args)  
+    {
+        Scanner in = new Scanner(System.in);
+        int n = in.nextInt();
+        if (isKeith(n))  
+            System.out.println("Yes, the given number is a Keith number.");  
+        else  
+            System.out.println("No, the given number is not a Keith number.");   
+    }  
+}