The famous Ramanujan constant $ e^{\pi \sqrt{163}} $ is a near-integer.
see the link here.
I tried to calculate this number with matlab and failed. Matlab cannot even deliver the first 9 apparently because of the double float precision.
2.625374126407683e+17
It seems that we need a customized algorithm. Could anyone give a hint?
Throwing this into Wolfram Alpha, my goto for stuff like this, I get
2.62537412640768743999999999999250072597198185688879353856337... × 10^17
with a continued fraction of
[262537412640768743; 1, 1333462407511, 1, 8, 1, 1, 5, 1, 4, 1, 7, 1, 1, 1, 9, 1, ...].