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 A188926 #6 Feb 08 2013 11:20:16 %S A188926 1,3,2,9,5,0,8,1,3,4,3,2,7,8,7,9,2,4,9,8,9,5,7,2,3,2,4,3,7,4,0,9,4,4, %T A188926 4,7,1,3,3,5,9,6,0,8,7,1,9,6,7,0,0,6,1,5,6,0,8,4,7,9,6,4,8,5,0,1,0,2, %U A188926 5,7,3,6,9,5,8,2,0,5,2,4,2,2,9,5,2,4,1,3,7,1,6,4,9,6,4,3,1,5,2,7,1,3,0,5,7,6,8,4,4,5,4,5,4,7,8,2,6,7,9,0,9,2,1,0,8,3,3,6,5,9 %N A188926 Decimal expansion of sqrt((7+sqrt(13))/6). %C A188926 Decimal expansion of the length/width ratio of a sqrt(1/3)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle. %C A188926 A sqrt(1/3)-extension rectangle matches the continued fraction [1,3,28,1,2,2,42,1,1,1,4,...] for the shape L/W=sqrt((7+sqrt(13))/6). 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 sqrt(1/3)-extension rectangle, 1 square is removed first, then 3 squares, then 28 squares, then 1 square,..., so that the original rectangle of shape sqrt((7+sqrt(13))/6) is partitioned into an infinite collection of squares. %e A188926 1.32950813432787924989572324374094447133596... %t A188926 r = 3^(-1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] %t A188926 N[t, 130] %t A188926 RealDigits[N[t, 130]][[1]] %t A188926 ContinuedFraction[t, 120] %t A188926 RealDigits[Sqrt[(7+Sqrt[13])/6],10,140][[1]] (* _Harvey P. Dale_, Feb 08 2013 *) %Y A188926 Cf. A188540, A188927. %K A188926 nonn,cons %O A188926 1,2 %A A188926 _Clark Kimberling_, Apr 13 2011