%I #12 Sep 08 2022 08:45:56
%S 2,7,7,5,5,1,5,6,5,7,8,8,6,6,8,0,3,7,1,6,2,6,2,1,1,5,0,3,1,5,6,5,7,9,
%T 3,0,1,2,5,7,7,1,4,1,5,5,0,1,0,4,4,6,9,3,9,7,5,1,1,9,7,2,3,0,9,2,6,4,
%U 5,7,4,6,5,7,9,2,7,5,8,2,3,8,1,7,4,1,4,4,9,0,7,4,6,1,5,4,8,3,8,0,2,2,6,1,9,8,4,6,1,6,6,0,8,6,0,7,0,7,0,3,9,5,8,6,5,0,4,3,2,3
%N Decimal expansion of (9+27*sqrt(2))/17.
%C The constant at A189960 is the shape of a rectangle whose continued fraction partition consists of 4 silver rectangles. For a general discussion, see A188635.
%H G. C. Greubel, <a href="/A189960/b189960.txt">Table of n, a(n) for n = 1..10000</a>
%F Continued fraction (as explained at A188635): [r,r,r,r], where r = 1 + sqrt(2). The ordinary continued fraction (as given by Mathematica program shown below) is as follows: [2,1,3,2,5,76,5,2,3,1,3,1,2,1,1,7,1,10,38,10,...]
%e 2.7755156578866803716262115031565793012577141550...
%t r = 1 + 2^(1/2);
%t FromContinuedFraction[{r,r,r,r}]
%t FullSimplify[%]
%t N[%, 150]
%t RealDigits[%] (*A189960*)
%t ContinuedFraction[%%, 120]
%t RealDigits[(9+27Sqrt[2])/17,10,150][[1]] (* _Harvey P. Dale_, Dec 22 2019 *)
%o (PARI) (9+27*sqrt(2))/17 \\ _G. C. Greubel_, Jan 13 2018
%o (Magma) (9+27*Sqrt(2))/17 // _G. C. Greubel_, Jan 13 2018
%Y Cf. A188635, A189959.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, May 02 2011