Add Happy Numbers (#2839)

Co-authored-by: Louve Le Bronec <loane.le.bronec@eisti.fr>
Co-authored-by: Yang Libin <contact@yanglibin.info>
Co-authored-by: Yang Libin <szuyanglb@outlook.com>

src/main/java/com/thealgorithms/others/HappyNumbersSeq.java

@@ -0,0 +1,35 @@
+package com.thealgorithms.others;
+
+import java.util.Arrays;
+import java.util.HashSet;
+import java.util.Scanner;
+import java.util.Set;
+
+public class HappyNumbersSeq {
+    private static final Set<Integer> CYCLE_NUMS = new HashSet<>(Arrays.asList(4, 16, 20, 37, 58, 145));
+
+    public static void main(String[] args) {
+        Scanner in = new Scanner(System.in);
+        System.out.print("Enter number: ");
+        int n = in.nextInt();
+        while (n != 1 && !isSad(n)) {
+            System.out.print(n + " ");
+            n = sumSquares(n);
+        }
+        String res = n == 1 ? "1 Happy number" : "Sad number";
+        System.out.println(res);
+    }
+
+    private static int sumSquares(int n) {
+        int s = 0;
+        for (; n > 0; n /= 10) {
+            int r = n % 10;
+            s += r * r;
+        }
+        return s;
+    }
+
+    private static boolean isSad(int n) {
+        return CYCLE_NUMS.contains(n);
+    }
+}