When an integer and its reversal are unequal, their product is never a square except when both are squares. A mathematical proof will be much appreciated. If the sum of the squares of the digits of n is less than 10 and n is not divisible by 10, then the product of n and the reversal of n is a palindrome. So this appears to be a palindrome. The table lists all the palindromes only upto length 9.
Larger ones are very easy to find.
Per given length their total number grows exponentially. That doesn't mean that we can't find some larger palindromes with beautiful patterns or special properties. On the contrary. I'd like to name these palindromes wing numbers, for obvious reason. 9 65.432 Infinite patterns are abundant here.