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%I #19 Sep 08 2022 08:45:56
%S 1,7,6,6,1,9,0,3,7,8,9,6,9,0,6,0,0,9,4,1,7,4,8,3,0,5,7,5,5,0,9,1,1,6,
%T 6,1,5,3,0,4,2,7,9,6,6,6,9,7,7,1,9,4,3,9,0,8,9,0,0,0,1,3,4,8,9,7,3,5,
%U 6,2,0,1,2,3,9,9,3,4,2,5,2,5,5,3,3,0,4,8,0,6,5,2,9,0,6,0,7,0,7,9,7,1,1,3,5,7,9,2,4,4,1,5,0,7,0,9,8,2,2,7,0,3,6,2,7,7,4,7,2,3
%N Decimal expansion of (3+sqrt(34))/5.
%C Decimal expansion of the length/width ratio of a (6/5)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle.
%C A (6/5)-extension rectangle matches the continued fraction [1,1,3,3,1,1,1,1,3,3,1,1,1,1,3,3,...] for the shape L/W=(3+sqrt(34))/5. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,1,...]. Specifically, for the (6/5)-extension rectangle, 1 square is removed first, then 1 square, then 3 squares, then 3 squares,..., so that the original rectangle of shape (3+sqrt(34))/5 is partitioned into an infinite collection of squares.
%H G. C. Greubel, <a href="/A188736/b188736.txt">Table of n, a(n) for n = 1..10000</a>
%e 1.76619037896906009417483057550911661530...
%p evalf((3+sqrt(34))/5,140); # _Muniru A Asiru_, Nov 01 2018
%t RealDigits[(3 + Sqrt[34])/5, 10, 111][[1]] (* _Robert G. Wilson v_, Aug 18 2011 *)
%o (PARI) (sqrt(34)+3)/5 \\ _Charles R Greathouse IV_, Apr 25 2016
%o (Magma) SetDefaultRealField(RealField(100)); (3 + Sqrt(34))/5; // _G. C. Greubel_, Nov 01 2018
%Y Cf. A188640.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Apr 12 2011
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