Lychrel Number Implementation

The Lychrel number is a mathematical concept that has been studied in the field of number theory. It was named after the mathematician John Lychrel, who discovered the property of this number.

A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly adding its own reverse to itself. The reverse of a number is obtained by reading it from right to left.

For example, let's consider the number 56:

• Reverse of 56: 65
• Add 56 and its reverse: 56 + 65 = 121 (which is a palindrome)

However, some numbers do not form a palindrome through this process, and these numbers are called Lychrel numbers.

For example, let's consider the number 196:

• Reverse of 196: 691
• Add 196 and its reverse: 196 + 691 = 887
• Reverse of 887: 788
• Add 887 and its reverse: 887 + 788 = 1675
• Reverse of 1675: 5761
• Add 1675 and its reverse: 1675 + 5761 = 7436
• Reverse of 7436: 6347
• Add 7436 and its reverse: 7436 + 6347 = 13783
• Reverse of 13783: 38731
• Add 13783 and its reverse: 13783 + 38731 = 52514
• Reverse of 52514: 41525
• Add 52514 and its reverse: 52514 + 41525 = 94039
• Reverse of 94039: 93049
• Add 94039 and its reverse: 94039 + 93049 = 187088
• Reverse of 187088: 880781
• Add 187088 and its reverse: 187088 + 880781 = 1067869
• Reverse of 1067869: 9687601
• Add 1067869 and its reverse: 1067869 + 9687601 = 10755470

After 24 iterations, the number 196 did not form a palindrome, and it is believed that it never will, no matter how many iterations are tried.

Here's an implementation of the Lychrel number in Python:

def is_lychrel_number(n):
    for i in range(50):
        n = n + int(str(n)[::-1])
        if str(n) == str(n)[::-1]:
            return False
    return True

This function checks if a number is a Lychrel number by performing up to 50 iterations of adding the number to its reverse, and checking if the result is a palindrome. If it is found that the number produces a palindrome, the function returns False, otherwise it returns True.

You can use this function to generate a list of Lychrel numbers:

lychrel_numbers = []
for i in range(10_000):
    if is_lychrel_number(i):
        lychrel_numbers.append(i)
print(lychrel_numbers)

This code will generate a list of Lychrel numbers between 1 and 10,000.

In summary, the Lychrel number is a fascinating mathematical concept with many properties waiting to be discovered. The implementation in Python provided here is just one way of exploring this concept, but there are many other ways to study and understand it further.