A188944 - OEIS

%I #4 Mar 30 2012 18:57:23

%S 4,5,1,4,1,6,2,2,9,6,4,5,1,3,6,4,6,9,8,3,2,7,9,4,7,4,8,7,8,6,9,1,3,1,

%T 9,1,4,2,9,9,1,3,6,0,5,6,3,9,1,8,3,2,7,3,2,1,0,5,5,5,1,8,0,2,6,6,3,1,

%U 0,3,9,2,2,5,6,5,7,2,1,2,4,0,7,9,8,6,9,0,3,7,8,4,1,8,1,8,7,9,6,4,6,1,6,4,5,1,4,0,5,5,3,8,3,4,1,7,8,9,6,8,0,8,5,4,9,0,0,3,7,1

%N Decimal expansion of (4-sqrt(7))/3.

%C Decimal expansion of the shape (= length/width = ((4-sqrt(7))/3) of the lesser (8/3)-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.

%e 0.45141622964513646983279474878691319142991360...

%t r = 8/3; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]

%t N[t, 130]

%t RealDigits[N[t, 130]][[1]]

%t ContinuedFraction[t, 120]

%Y Cf. A188738, A188945.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Apr 14 2011