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%I #13 Dec 15 2022 15:31:10
%S 1,6,4,0,3,8,8,2,0,3,2,0,2,2,0,7,5,6,8,7,2,7,6,7,6,2,3,1,9,9,6,7,5,9,
%T 6,2,8,1,4,3,3,9,9,9,0,3,1,7,1,7,0,2,5,5,4,2,9,9,8,2,9,1,9,6,6,3,6,8,
%U 6,9,2,9,3,2,9,2,2,0,2,6,9,9,1,9,8,4,8,2,9,5,6,3,5,1,3,3,5,5,3,7,0,8,5,5,6,8,0,0,5,1,1,7,4,0,1,7,6,7,7,0,1,9,1,2,6,7,7,6,0,5
%N Decimal expansion of (9+sqrt(17))/8.
%C Decimal expansion of the shape (= length/width = ((9+sqrt(17))/8) of the greater (9/4)-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.
%C This number - 1, namely w = (1 + sqrt(17))/8 = 0.6403882032..., is the positive real root of 4*x^2 - x - 1, with negative root -(-1 + sqrt(17))/8 = -0.3903882032... = -(w - 1/4). - _Wolfdieter Lang_, Dec 12 2022
%e 1.64038820320220756872767623199675962814339990...
%t r = 9/4; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][[1]]
%t ContinuedFraction[t, 120]
%o (PARI) (sqrt(17)+9)/8 \\ _Charles R Greathouse IV_, Apr 25 2016
%Y Cf. A188738, A189037.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Apr 15 2011
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