%I #12 Sep 11 2023 12:58:05

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

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

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

%N Decimal expansion of 3*(1 + 3*sqrt(5))/11.

%C The constant at A189961 is the shape of a rectangle whose continued fraction partition consists of 4 golden rectangles. For a general discussion, see A188635.

%H G. C. Greubel, <a href="/A189962/b189962.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(5))/2. Ordinary continued fraction, as given by Mathematica program shown below:

%F [2,9,1,3,1,1,3,9,1,3,1,1,3,9,1,3,1,1,3,...]

%e 2.10223743613619156978932391078013510172414229422761...

%t r=(1+5^(1/2))/2;

%t FromContinuedFraction[{r,r,r,r}]

%t FullSimplify[%]

%t N[%,130]

%t RealDigits[%] (*A189962*)

%t ContinuedFraction[%%]

%t RealDigits[3 (1+3*Sqrt[5])/11,10,150][[1]] (* _Harvey P. Dale_, Sep 11 2023 *)

%o (PARI) 3*(1+3*sqrt(5))/11 \\ _G. C. Greubel_, Jan 13 2018

%o (Magma) 3*(1+3*Sqrt(5))/11 // _G. C. Greubel_, Jan 13 2018

%Y Cf. A188635, A189961, A189963.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, May 02 2011

%E Definition corrected by _G. C. Greubel_, Jan 13 2018