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 A188935 #14 Jul 04 2023 03:27:55 %S A188935 1,1,8,0,4,6,0,4,2,1,7,1,6,3,6,9,9,4,8,1,6,6,6,1,4,0,4,0,8,6,7,0,1,1, %T A188935 1,7,7,0,1,4,1,6,1,6,8,2,4,6,4,4,0,1,8,6,4,4,0,3,1,9,2,1,7,4,4,1,4,3, %U A188935 8,8,7,8,7,5,5,3,1,5,1,7,0,6,6,3,3,8,4,4,4,0,4,6,5,9,6,4,1,4,4,3,9,0,5,1,5,5,8,5,0,1,5,0,8,5,5,1,9,3,9,5,5,5,8,9,6,7,7,1,7,9 %N A188935 Decimal expansion of (1+sqrt(37))/6. %C A188935 Decimal expansion of the length/width ratio of a (1/3)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle. %C A188935 A (1/3)-extension rectangle matches the continued fraction [1,5,1,1,5,1,1,5,1,1,5,...] for the shape L/W=(1+sqrt(37))/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 (1/3)-extension rectangle, 1 square is removed first, then 5 squares, then 1 square, then 1 square,..., so that the original rectangle of shape (1+sqrt(37))/6 is partitioned into an infinite collection of squares. %F A188935 Equals exp(arcsinh(1/6)). - _Amiram Eldar_, Jul 04 2023 %e A188935 1.1804604217163699481666140408670111770141616824644... %t A188935 RealDigits[(1 + Sqrt[37])/6, 10, 111][[1]] (* _Robert G. Wilson v_, Aug 18 2011 *) %Y A188935 Cf. A188640, A188934. %K A188935 nonn,cons %O A188935 1,3 %A A188935 _Clark Kimberling_, Apr 13 2011