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# What are lychrel numbers?

Ayesha Naeem

Lychrel numbers are natural numbers that can never form a palindrome after an iterative process of adding the number to its reverse. The first few numbers that fail to form a palindrome are known as lychrel numbers.

## Method

• To determine if a number is lychrel, check if the number is a palindrome or not.
• If the number is a palindrome, the number is not a lychrel; otherwise, the number is added to its reverse and the new number is checked as a palindrome.
• The process is repeated until a palindrome is found.
• For example, the number 35 is not a palindrome. In the first iteration, 35 is added to 53 to form 88. The number 88 is a palindrome, therefore it takes one iteration to prove that 35 is not a lychrel.

## Implementation

The following code demonstrates how to find lychrel numbers in C++:

#include <iostream>
using namespace std;

int reverse(int num)
{
int reversed = 0;
while(num>0)
{
int mod = num%10;
reversed = (reversed*10) + mod;
num = num/10;

}
return reversed;
}

void isLychrel(int num, int max)
{
//variable that holds 0 if lychrel and 1 if not
int lychrel = 0;
//duplicate the number for checking later
int num_temp=num;

while(num>0)
{
// get the reverse
int palindrome = reverse(num);
// compare with original
if(palindrome == num)
{
// set the check to 1 and exit loop
lychrel = 1;
break;
}
// if not a palindrom, reverse the number and add to the original number
num = reverse(num) + num;
// decrease the iteration count
max--;
}
// display results
if(lychrel)
{
cout<< "The number "<<num_temp<<" is not lycheral."<<endl;
}
else
{
cout<< "The number "<<num_temp<<" is lycheral."<<endl;
}
}

int main() {

int max = 10;
int num_1 = 35;
int num_2 = 295;
//check if the number is lychrel or not
isLychrel(num_1, max);
isLychrel(num_2, max);

}

## Explanation

For the sake of implementation, the above code uses a maximum number to limit the iterations. If a palindrome is found within the limit, it is not lychrel.

• The program is implemented for two numbers, 35 and 295.
• The program calls the isLychrel function, which performs iterations until it finds a palindrome or reaches the maximum limit of iterations.
• The isLychrel function calls the reverse function and compares the returned value with the original value to check if the original number is a palindrome or not.
• If the number is not a palindrome, the program calls the reverse function again, adds the returned value to the original number, and repeats the process.

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Ayesha Naeem