Every positive integer can be written as the sum of three palindromes, numbers that remain the same when their digits are reverse. For example, 389 = 11 + 55 + 323. This holds not just for base 10 but for any base b ≥ 5.
[Update: a new paper on arXiv extends this to b = 3 and 4 as well. Base 2 requires four palindromes.]
The result and algorithms for finding the palindromes was published online last August and is in the most recent print issue of Mathematics of Computation.
Javier Cilleruelo, Florian Luca and Lewis Baxter. Every positive integer is a sum of three palindromes. DOI: https://doi.org/10.1090/mcom/3221