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A189959 Decimal expansion of (4+5*sqrt(2))/4.

%I A189959 #19 Dec 17 2024 13:02:19
%S A189959 2,7,6,7,7,6,6,9,5,2,9,6,6,3,6,8,8,1,1,0,0,2,1,1,0,9,0,5,2,6,2,1,2,2,
%T A189959 5,9,8,2,1,2,0,8,9,8,4,4,2,2,1,1,8,5,0,9,1,4,7,0,8,4,9,6,7,2,4,8,8,4,
%U A189959 1,5,5,9,8,0,7,7,6,3,3,7,9,8,5,6,2,9,8,4,4,1,7,9,0,9,5,5,1,9,6,5,9,1,8,7,6,7,3,0,7,7,8,8,6,4,0,3,7,1,2,8,1,1,5,6,0,4,5,0,6,9
%N A189959 Decimal expansion of (4+5*sqrt(2))/4.
%C A189959 Essentially the same as A020789. - _R. J. Mathar_, May 16 2011
%C A189959 The constant at A189959 is the shape of a rectangle whose continued fraction partition consists of 3 silver rectangles.  For a general discussion, see A188635.
%H A189959 G. C. Greubel, <a href="/A189959/b189959.txt">Table of n, a(n) for n = 1..10000</a>
%F A189959 Continued fraction (as explained at A188635): [r,r,r], where r = 1 + sqrt(2). The ordinary continued fraction (as given by Mathematica program shown below) is as follows:
%F A189959 [2,1,3,3,3,1,2,1,3,3,3,1,2,1,3,3,3,1,2,1,3,3,3,1,2...]
%e A189959 2.767766952966368811002110905262122598212089844221...
%t A189959 r=1+2^(1/2);
%t A189959 FromContinuedFraction[{r,r,r}]
%t A189959 FullSimplify[%]
%t A189959 N[%,130]
%t A189959 RealDigits[%]
%t A189959 ContinuedFraction[%%]
%t A189959 RealDigits[(4+5Sqrt[2])/4,10,150][[1]] (* _Harvey P. Dale_, Dec 17 2024 *)
%o A189959 (PARI) (4+5*sqrt(2))/4 \\ _G. C. Greubel_, Jan 13 2018
%o A189959 (Magma) (4+5*Sqrt(2))/4 // _G. C. Greubel_, Jan 13 2018
%Y A189959 Cf. A188635.
%K A189959 nonn,cons
%O A189959 1,1
%A A189959 _Clark Kimberling_, May 02 2011