%N Decimal expansion of sqrt(3) - Pi/2.
%C Decimal expansion of the real number quantifying the area of the Apollonian gasket of three congruent circles of radius 1.
%C General solution: This constant is the ratio of r^2, where r is the radius of three congruent circles forming a Apollonian gasket, to the area of that Apollonian gasket.
%C sqrt(3)-pi/2 is the area enclosed between three identical osculating circles of unit radius. - _Lekraj Beedassy_, Apr 12 2006
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ApollonianGasket.html">Apollonian Gasket</a>.
%F a(n) = 3^(1/2) - pi/2.
%e RealDigits[ Sqrt - Pi/2, 10, 105][]
%t RealDigits[N[Sqrt - Pi/2, 300]][] (* _Vladimir Joseph Stephan Orlovsky_, Jul 03 2011 *)
%Y Cf. A002194; A019669.
%A Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Feb 01 2004
%E More terms from _Robert G. Wilson v_, Feb 09 2004
%E Edited by _N. J. A. Sloane_, Jul 05 2008 at the suggestion of _Rick L. Shepherd_