Is it the original seat post? I've worked for bike co-ops and have rehabed quite a few bikes over the years. Every once in a while you will find that someone has replaced a seat post with one that seemed "close enough". There are numerous seatpost sizes available and some are very close in size. If you don't have a good caliper, find a bike shop or other mechanic who has one and measure both the tube and the post. Don't try it with a tape measure as you are unlikely to get an accurate reading.
In lieu of a new seat post, you might be able to use a shim to snug things up. A clamp above the seat tube is another option to keep your post from sliding down, but it doesn't solve the problem of a loose post turning too easily which can be a nuisance.