The Rev Dodgson said:

And talking of strangely defined sequences of numbers in base 10:

Do any base-10 Lychrel numbers exist?
Supercomputers have spent decades expanding a single number into a billion-digit monster, yet they still cannot solve the simple addition puzzle behind it.

The puzzle goes like this: take a number, reverse its digits, and add the two together. If a person takes the number 56 and reverses it to 65, adding them together yields 121, which is a palindrome. Most numbers will eventually form a palindrome after just a few iterations of this reverse-and-add process. A number that never forms a palindrome, no matter how many times the process is repeated, is called a Lychrel number.

To answer the question directly: it is currently unknown if any base-10 Lychrel numbers actually exist. Mathematicians have never been able to definitively prove that a specific base-10 number will infinitely avoid becoming a palindrome. However, there are very strong suspicions that they do exist, primarily centered around one famous candidate: the number 196.

When computers apply the reverse-and-add process to 196, the numbers quickly spiral out of control. Over the decades, programmers and mathematicians have run 196 through sophisticated algorithms, taking the process through hundreds of millions of iterations. While the resulting sum has swollen to over a billion digits long, it has never formed a palindrome. Despite this massive computational evidence, a true mathematical proof confirming that 196 is a Lychrel number remains elusive. Until someone can write a proof showing that it will never happen, it is entirely possible that a palindrome is waiting at the two-billionth iteration.

Interestingly, this mystery is entirely specific to base-10. Mathematicians have successfully proven that Lychrel numbers definitely exist in other numeral systems, such as base-2 (binary). Yet, because no mathematical proof exists for base-10, numbers like 196, 295, and 394 are officially classified merely as “candidate” Lychrel numbers. They sit in a strange computational limbo, heavily suspected to be Lychrel numbers, but eternally waiting for a rigorous proof.

thanks don’t think we heard of that before