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%I #8 Oct 02 2022 23:20:34
%S 2,2,7,9,6,1,0,3,7,3,1,1,0,5,1,2,6,2,6,6,0,2,0,1,6,8,7,6,9,1,6,1,7,3,
%T 3,6,2,3,0,0,2,0,8,4,3,6,2,2,8,5,2,0,1,3,8,2,1,8,0,9,2,0,6,6,7,0,6,9,
%U 8,7,8,6,2,1,7,8,3,6,6,8,0,9,1,2,4,3
%N Decimal expansion of (e+sqrt(-4+e^2))/2.
%C Decimal expansion of the shape (= length/width = ((e+sqrt(-4+e^2))/2) of the greater e-contraction rectangle.
%C See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 2.2796103731105126266020168769161733623002084362...
%t r = E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][[1]]
%t ContinuedFraction[t, 120]
%t RealDigits[(E+Sqrt[E^2-4])/2,10,150][[1]] (* _Harvey P. Dale_, Oct 17 2013 *)
%Y Cf. A188738, A189040, A189041.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Apr 15 2011
%E Corrected by _Harvey P. Dale_, Oct 17 2013
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