Lychrel Number in Java

A Lychrel Number is a number that never forms a palindrome even after repeatedly applying the Reverse + Add process. Although no number has been mathematically proven to be a true Lychrel Number, certain numbers (like 196) are famous because no palindrome has ever formed, even after millions of iterations.

In programming, we use a practical definition:
If a number does not form a palindrome within 500 Reverse + Add iterations, we consider it a Lychrel candidate.

What is the Reverse + Add Process?

• Take a number
• Reverse the digits
• Add the reversed number to the original
• If the result becomes a palindrome → Not a Lychrel Number
• If no palindrome appears within the limit → Lychrel candidate

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Example 1: 56

• Step 1: Reverse 56 → 65
• 56 + 65 = 121

Since 121 is a palindrome, 56 is NOT a Lychrel Number.

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Example 2: 89 (A Very Interesting Case)

89 is known for taking 24 iterations to reach a palindrome.

• Step 1: 89 + 98 = 187
• Step 2: 187 + 781 = 968
• Step 3: 968 + 869 = 1837
• … continues …
• Final: 8813200023188 (palindrome)

So 89 is NOT a Lychrel Number, though it behaves like one for a while.

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Example 3: 196 – The Famous Suspected Lychrel Number

The number 196 is the most famous Lychrel candidate. Despite millions of Reverse + Add iterations tested by mathematicians and supercomputers, no palindrome has ever been found.

This makes 196 an excellent example for Lychrel behavior in programming tasks.

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Full Dry Run Example

Let’s take a small number and trace all the steps clearly.

Example: 4

• Step 1: Reverse 4 → 4, so 4 + 4 = 8
• Step 2: Reverse 8 → 8, so 8 + 8 = 16
• Step 3: Reverse 16 → 61 → 16 + 61 = 77
• 77 is a palindrome

Therefore, 4 is NOT a Lychrel Number.

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Java Program to Check Lychrel Number

public class LychrelNumber {

    // Reverse a number
    static long reverse(long n) {
        long rev = 0;
        while (n > 0) {
            rev = rev * 10 + n % 10;
            n /= 10;
        }
        return rev;
    }

    // Check if a number is palindrome
    static boolean isPalindrome(long n) {
        return n == reverse(n);
    }

    // Check if a number is a Lychrel candidate
    static boolean isLychrel(long n) {
        long temp = n;

        for (int i = 0; i < 500; i++) {
            long rev = reverse(temp);
            temp = temp + rev;

            if (isPalindrome(temp)) {
                return false; // Not a Lychrel Number
            }
        }

        return true; // Lychrel candidate
    }

    public static void main(String[] args) {
        long n = 196;

        if (isLychrel(n))
            System.out.println(n + " is a Lychrel Number");
        else
            System.out.println(n + " is NOT a Lychrel Number");
    }
}
  

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Practice Challenges

1. Write a Java program to: Print every step of the Reverse + Add process until a palindrome is found (or until 500 iterations).
2. Modify the program to: Count the exact number of iterations required to form a palindrome.
3. For numbers from 1 to 500: Print all Lychrel candidates based on the 500-iteration limit.