Today, Andy told us about an almost integer, $e^ {\pi \sqrt {163}}$. I just did some quick googling to find out how many decimal places it had while still being rounded to an integer. It turns out the number, called Ramanujan's Constant, is 262,537,412,640,768,743.99999999999925…, which rounds to an integer within 12 decimal places. I found a website that talks not only about Ramanujan's Constant, but other variations of it that all involve $e$ and $\pi$. The website is here if you're interested.

I also found another website full of a bunch of other almost integers. Though some of them are a bit ridiculous — almost integer (8) involves taking the cosine of the cosine of the cosine … of the cosine (I think I counted seven times) of 5 and just multiplying it by two — there are other simpler ones. The website is here if you're interested.