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 A188930 #8 Nov 06 2014 04:37:39 %S A188930 4,6,8,5,5,5,7,7,2,0,2,8,2,9,6,7,7,9,4,6,0,6,4,5,7,7,4,3,4,3,7,1,6,7, %T A188930 6,2,7,4,0,6,5,6,5,8,4,0,2,6,8,1,9,5,8,5,2,7,0,3,5,8,9,8,1,2,6,6,1,4, %U A188930 8,1,3,0,3,0,9,5,1,1,9,9,2,5,9,5,4,2,7,3,8,4,1,4,8,3,4,2,2,5,0,9,7,8,8,1,0,2,7,7,7,3,7,7,3,8,7,9,7,2,6,2,9,1,1,2,1,3,3,1,8,4 %N A188930 Decimal expansion of sqrt(5)+sqrt(6). %C A188930 Decimal expansion of the length/width ratio of a sqrt(20)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle. %C A188930 A sqrt(20)-extension rectangle matches the continued fraction [4,1,2,5,1,1,4,1,2,24,1,2,...] for the shape L/W=sqrt(5)+sqrt(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(20)-extension rectangle, 4 squares are removed first, then 1 square, then 2 squares, then 5 squares,..., so that the original rectangle of shape sqrt(5)+sqrt(6) is partitioned into an infinite collection of squares. %e A188930 4.6855577202829677946064577434371676274... %t A188930 r = 48^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] %t A188930 N[t, 130] %t A188930 RealDigits[N[t, 130]][[1]] %t A188930 ContinuedFraction[t, 120] %t A188930 RealDigits[Sqrt[5]+Sqrt[6],10,150][[1]] (* _Harvey P. Dale_, Nov 06 2014 *) %Y A188930 Cf. A188640, A188931. %K A188930 nonn,cons %O A188930 1,1 %A A188930 _Clark Kimberling_, Apr 13 2011