OFFSET
1,1
COMMENTS
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.
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...
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
2.850781059358212171622054418655453316130105033155254721...
MAPLE
evalf((5+sqrt(41))/4, 140); # Muniru A Asiru, Nov 01 2018
MATHEMATICA
r = 5/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
PROG
(PARI) default(realprecision, 100); (5+sqrt(41))/4 \\ G. C. Greubel, Nov 01 2018
(Magma) SetDefaultRealField(RealField(100)); (5+Sqrt(41))/4; // G. C. Greubel, Nov 01 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 10 2011
STATUS
approved