A188731 - OEIS

%I #13 Sep 08 2022 08:45:56

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

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

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

%N Decimal expansion of (5+sqrt(41))/4.

%C Decimal expansion of shape of a (5/2)-extension rectangle; see A188640 for definitions of shape and r-extension rectangle.  Briefly, shape=length/width, and an r-extension rectangle is composed of two rectangles of shape r.

%C The continued fractions of the constant are 2, 1, 5, 1, 2, 2, 1, 5, 1, 2, 2, 1, 5, 1, 2, 2, 1, 5, 1...

%H G. C. Greubel, <a href="/A188731/b188731.txt">Table of n, a(n) for n = 1..10000</a>

%e 2.850781059358212171622054418655453316130105033155254721...

%p evalf((5+sqrt(41))/4,140); # _Muniru A Asiru_, Nov 01 2018

%t r = 5/2; 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) default(realprecision, 100); (5+sqrt(41))/4 \\ _G. C. Greubel_, Nov 01 2018

%o (Magma) SetDefaultRealField(RealField(100)); (5+Sqrt(41))/4; // _G. C. Greubel_, Nov 01 2018

%Y Cf. A188640.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Apr 10 2011