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Decimal expansion of (e+sqrt(-4+e^2))/2.
4

%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