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%I #14 Sep 08 2022 08:45:56
%S 2,1,8,6,1,4,0,6,6,1,6,3,4,5,0,7,1,6,4,9,6,2,6,5,2,8,6,7,0,5,4,7,3,2,
%T 3,2,9,5,5,5,0,6,6,1,1,4,4,9,5,6,9,8,0,9,1,9,2,4,9,6,9,3,6,7,6,4,1,4,
%U 7,5,1,8,0,3,6,4,3,5,1,1,5,6,7,5,6,7,8,1,3,4,1,3,9,9,1,9,7,0,3,0,6,0,4,8,8,9,3,6,9,2,3,6,4,1,2,7,0,9,4,6
%N Decimal expansion of (3+sqrt(33))/4, which has periodic continued fractions [2,5,2,1,2,5,2,1,...] and [3/2, 1, 3/2, 1, ...].
%C Let R denote a rectangle whose shape (i.e., length/width) is (3+sqrt(33))/4. This rectangle can be partitioned into squares in a manner that matches the continued fraction [2,5,2,1,2,5,2,1,2,5,2,1,...]. It can also be partitioned into rectangles of shape 3/2 and 3 so as to match the continued fraction [3/2, 1, 3/2, 1, 3/2, ...]. For details, see A188635.
%C Apart from the first digit, the same as A188939. - _R. J. Mathar_, May 16 2011
%H G. C. Greubel, <a href="/A189966/b189966.txt">Table of n, a(n) for n = 1..10000</a>
%e 2.18614066163450716496265286705473232955506611449...
%t FromContinuedFraction[{3/2, 1, {3/2, 1}}]
%t ContinuedFraction[%, 25] (* [2,5,2,1,2,5,2,1,...] *)
%t RealDigits[N[%%, 120]] (* A189966 *)
%t N[%%%, 40]
%o (PARI) (3+sqrt(33))/4 \\ _G. C. Greubel_, Jan 12 2018
%o (Magma) (3+Sqrt(33))/4 // _G. C. Greubel_, Jan 12 2018
%Y Cf. A188635, A188485.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, May 05 2011
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