OFFSET
1,1
COMMENTS
Decimal expansion of shape of a (9/4)-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 (periodic) continued fraction of the constant is [2,1,1,1,2,2,1,1,1,2,2,1,...].
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
2.6301993223490369350160301287973260065531690506317...
MAPLE
evalf((9+sqrt(145))/8, 120); # Muniru A Asiru, Nov 01 2018
MATHEMATICA
r = 9/4; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
PROG
(PARI) (9+sqrt(145))/8 \\ Michel Marcus, Sep 03 2014
(Magma) SetDefaultRealField(RealField(100)); (9+Sqrt(145))/8; // G. C. Greubel, Nov 01 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 10 2011
STATUS
approved