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A189042 Decimal expansion of (e-sqrt(-4+e^2))/2. 0


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

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

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

%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 lesser 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.

%e 0.4386714553485326087582705944364891354570...

%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]

%o (PARI) (exp(1)-sqrt(exp(2)-4))/2 \\ _Charles R Greathouse IV_, Apr 25 2016

%Y Cf. A188738, A189040, A189041.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Apr 15 2011

%E a(129) corrected by _Georg Fischer_, Apr 04 2020

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)