What are the numbers that can be expressed as the sum of two palindromes?
A number is a palindrome if it is the same written backwards, like 1367631.
My motivation comes from the problem posed for some given numbers in a grade 4 math competition.
However, a bit of searching revealed that similar questions have been studied a lot.
It has been a long-standing conjecture that every number is the sum of three palindromes, proved in Javier Cilleruelo, Florian Luca and Lewis Baxter: Every positive integer is a sum of three palindromes, Math. Comp. 87 (2018), 3023-3055.
It is not hard to find numbers that are not the sum of two palindromes.
But do they have a nice characterization?
What is the simplest algorithm to decide if an input number is the sum of two palindromes or not?
