Answer to 'Past the decimal point'

[Click here to read the question.]

As you may have deduced from the MathWorld article I referenced, the answer is almost an integer, but not quite. Thus the answer '163' is incorrect.

Here's the catch: even though a quick look at the expression hints that the answer is not an integer (or even rational), most calculators and computers will tell you that the answer is 163. This should have raised a red flag in your mind, and led to more careful analysis/computation. Here's the answer to 35 decimal places, as generated by Mathematica:

163.00000000000000000000000000002322

As you can see, this number doesn't diverge from 163 until after the 30th decimal place. If you're not careful, even Mathematica will incorrectly give you 163. For this post, I had to explicitly tell Mathematica how much precision I needed. For the morbidly curious, here's the answer to 200 decimal places:

163.0000000000000000000000000000232167779424533410679
7849303647979599552603958882248257256551353136720534
306763983716241556818691116559260618916795700533302
716713392783181506705567740276991223717742914