If you also take the cards modulo 13 for their face, this approach works. 4 and 13 are relatively prime, so each number between 1 and 52 can be uniquely repres

If you also take the cards modulo 13 for their face, this approach works. 4 and 13 are relatively prime, so each number between 1 and 52 can be uniquely represented by the function (x) -> (x%13, x%4).