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A189963 Decimal expansion of (5+9*sqrt(5))/12.

%I A189963 #9 Sep 08 2022 08:45:56
%S A189963 2,0,9,3,7,1,7,6,4,9,7,9,1,5,0,8,9,3,8,9,7,3,5,4,6,9,1,8,2,1,5,1,2,3,
%T A189963 8,4,3,2,4,7,1,3,0,4,3,6,3,7,5,3,1,0,9,5,9,8,6,9,8,3,9,6,0,0,7,2,4,5,
%U A189963 5,7,3,6,0,8,9,5,0,2,0,3,4,1,2,2,7,4,7,7,4,7,2,9,5,0,7,5,3,3,7,2,8,9,3,7,9,7,7,9,8,7,7,9,7,4,7,0,0,4,2,9,4,8,5,6,6,1,7,4,6,0
%N A189963 Decimal expansion of (5+9*sqrt(5))/12.
%C A189963 The constant at A189963 is the shape of a rectangle whose continued fraction partition consists of 5 golden rectangles.  For a general discussion, see A188635.
%H A189963 G. C. Greubel, <a href="/A189963/b189963.txt">Table of n, a(n) for n = 1..10000</a>
%F A189963 Continued fraction (as explained at A189959): [r,r,r,r,r], where r=(1+sqrt(5))/2.  Ordinary continued fraction, as given by Mathematica program shown below:
%F A189963 [2,10,1,2,29,1,5,2,1,1,2,1,3,5,1,3,3,10,1,2,29,...].
%e A189963 2.09371764979150893897354691821512384324713043637531095986983...
%t A189963 r=(1+5^(1/2))/2;
%t A189963 FromContinuedFraction[{r,r,r,r,r}]
%t A189963 FullSimplify[%]
%t A189963 N[%,130]
%t A189963 RealDigits[%]  (*A189963*)
%t A189963 ContinuedFraction[%%]
%o A189963 (PARI) (5+9*sqrt(5))/12 \\ _G. C. Greubel_, Jan 13 2018
%o A189963 (Magma) (5+9*Sqrt(5))/12 // _G. C. Greubel_, Jan 13 2018
%Y A189963 Cf. A188635, A189961, A189962.
%K A189963 nonn,cons
%O A189963 1,1
%A A189963 _Clark Kimberling_, May 02 2011