What is the song played in the beginning of episode 13 of Parasyte: the Maxim at 00:00:29? Please be specific. It's quite close to "Next to You", and has a tune that was played when Kana first saw Shinichi in and got freaked out, in pure piano (synthesizer), but with a different tempo/speed/etc. And I'm sure it's not "Next to You".
I believe that the tune you are looking for is Next to You-Anime Version. This one is different from the Original One in the aspects of being slower and softer, and with a totally different instrument playing it and from the other Anime Version in the same terms.
Unfortunately, I haven't been able to find it in any of the OSTs. It might be an unreleased track for an unreleased OST like Krazer said, but that's anyone's guess.