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A188739 Decimal expansion of e+sqrt(e^2-1). 7

%I

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

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

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

%N Decimal expansion of e+sqrt(e^2-1).

%C Decimal expansion of the shape of a greater 2e-contraction rectangle; see A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and the partitioning of these rectangles into sets of squares in a manner that matches the continued fractions of their shapes.

%H G. C. Greubel, <a href="/A188739/b188739.txt">Table of n, a(n) for n = 1..10000</a>

%F e+sqrt(-1+e^2), with continued fraction A188627.

%e 5.24594005277075985646114668616376972685147198530... = 1/A188738 .

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

%t N[t, 130]

%t RealDigits[N[t, 130]][[1]] (* A188739 *)

%t ContinuedFraction[t, 120] (* A188627 *)

%o (PARI) default(realprecision, 100); exp(1) + sqrt(exp(2) - 1) \\ _G. C. Greubel_, Nov 01 2018

%o (MAGMA) SetDefaultRealField(RealField(100)); Exp(1) + Sqrt(Exp(2) -1); // _G. C. Greubel_, Nov 01 2018

%Y Cf. A188738 (inverse), A188627 (continued fraction).

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Apr 11 2011

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)