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 A188656 #19 Apr 28 2021 04:27:33 %S A188656 1,1,3,2,7,8,2,2,1,8,5,3,7,3,1,8,7,0,6,5,4,5,8,2,6,6,5,3,7,8,7,9,7,1, %T A188656 3,9,1,3,9,1,7,9,9,5,3,8,2,0,1,0,7,1,6,7,3,4,9,2,0,7,4,0,4,8,6,5,7,9, %U A188656 8,4,3,6,8,8,7,8,2,1,1,0,2,5,3,7,0,0,1,9,2,8,3,3,3,9,6,5,3,8,3,0,4,5,4,6,8,0,3,0,8,2,6,7,4,9,3,2,3,9,0,2,6,7,1,8,5,8,1,5,1,5 %N A188656 Decimal expansion of (1+sqrt(65))/8. %C A188656 Apart from the second digit the same as A177707. %C A188656 Decimal expansion of the shape of a (1/4)-extension rectangle. %C A188656 See A188640 for definitions of shape and r-extension rectangle. %C A188656 A (1/4)-extension rectangle matches the continued fraction [1,7,1,1,7,1,1,7,1,1,7,1,1,7,...] for the shape L/W= (1+sqrt(65))/8. 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 7 squares, then 1 square, then 1 square, then 7 squares,..., so that the original rectangle is partitioned into an infinite collection of squares. %H A188656 Daniel Starodubtsev, <a href="/A188656/b188656.txt">Table of n, a(n) for n = 1..10000</a> %H A188656 Clark Kimberling, <a href="http://www.jstor.org/stable/27963362">A Visual Euclidean Algorithm</a>, The Mathematics Teacher 76 (1983) 108-109. %e A188656 length/width = 1.13278221853731870654582665.... %t A188656 RealDigits[(1 + Sqrt[65])/8, 10, 111][[1]] (* _Robert G. Wilson v_, Aug 19 2011 *) %Y A188656 Cf. A188640, A105395. %K A188656 nonn,cons %O A188656 1,3 %A A188656 _Clark Kimberling_, Apr 09 2011