This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A188655 #27 Apr 28 2021 04:27:20 %S A188655 1,8,6,8,5,1,7,0,9,1,8,2,1,3,2,9,7,6,4,3,7,3,0,7,3,7,5,5,8,2,3,4,9,8, %T A188655 6,4,8,7,5,0,4,3,2,1,9,1,2,8,1,7,4,8,7,3,7,5,7,0,1,5,1,0,1,8,7,4,2,3, %U A188655 8,8,9,8,2,7,6,4,3,3,6,8,1,5,0,6,8,2,0,6,3,6,0,6,7,2,8,3,0,2,3,9,2,2,4,5,0,4,7,2,7,3,4,1,3,5,4,5,1,3,4,5,8,6,7,6,8,9,2,7,5,4 %N A188655 Decimal expansion of (2+sqrt(13))/3. %C A188655 Decimal expansion of the length/width ratio of a (4/3)-extension rectangle. %C A188655 See A188640 for definitions of shape and r-extension rectangle. %C A188655 A (4/3)-extension rectangle matches the continued fraction [1,1,6,1,1,1,1,6,1,1,1,1,6,...] for the shape L/W= (2+sqrt(13))/3. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,...]. Specifically, for the (4/3)-extension rectangle, 1 square is removed first, then 1 square, then 6 squares, then 1 square, then 1 square,..., so that the original rectangle is partitioned into an infinite collection of squares. %H A188655 Daniel Starodubtsev, <a href="/A188655/b188655.txt">Table of n, a(n) for n = 1..10000</a> %H A188655 Clark Kimberling, <a href="http://www.jstor.org/stable/27963362">A Visual Euclidean Algorithm</a>, The Mathematics Teacher 76 (1983) 108-109. %e A188655 length/width = 1.868517091821329764373.... %t A188655 r = 4/3; t = (r + (4 + r^2)^(1/2))/2; RealDigits[ N[ FullSimplify@ t, 111]][[1]] %t A188655 RealDigits[(2 + Sqrt@ 13)/3, 10, 111][[1]] (* Or *) %t A188655 RealDigits[Exp@ ArcSinh[2/3], 10, 111][[1]] (* _Robert G. Wilson v_, Aug 17 2011 *) %Y A188655 Cf. A188640, A010122. %K A188655 nonn,cons %O A188655 1,2 %A A188655 _Clark Kimberling_, Apr 09 2011 %E A188655 a(130) corrected by _Georg Fischer_, Apr 01 2020