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 A188724 #19 Jul 17 2021 02:39:14 %S A188724 2,0,5,6,9,5,2,4,3,8,7,1,0,9,6,5,9,0,9,3,9,6,7,8,7,9,2,4,3,7,8,8,0,7, %T A188724 2,5,8,5,8,8,0,9,9,1,4,1,5,4,9,7,1,7,6,2,0,4,6,7,6,4,2,6,8,3,4,1,6,1, %U A188724 9,5,6,5,7,6,0,3,4,1,7,4,6,1,3,2,2,1,8,2,6,6,1,4,5,7,6,5,0,2,1,5,1,8,9,6,9,9,2,5,3,9,6,2,4,2,1,0,6,6,2,4,8,0,9,8,2,4,8,8,4,1,9,8 %N A188724 Decimal expansion of shape of a (Pi/2)-extension rectangle; shape = (1/4)*(Pi + sqrt(16 + Pi^2)). %C A188724 See A188640 for definitions of shape and r-extension rectangle. Briefly, an r-extension rectangle is composed of two rectangles of shape r. %C A188724 A (Pi/2)-extension rectangle matches the continued fraction [2,17,1,1,3,1,3,2,2,1637,1,210,7,...] of the shape L/W = (1/4)*(Pi + sqrt(16 + Pi^2)). This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,...]. Specifically, for the (Pi/2)-extension rectangle, 2 squares are removed first, then 17 squares, then 1 square, then 1 square, then 3 squares, ..., so that the original rectangle is partitioned into an infinite collection of squares. %H A188724 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %e A188724 2.0569524387109659093967879243788072585880991... %t A188724 r = Pi/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] %t A188724 N[t, 130] %t A188724 RealDigits[N[t, 130]][[1]] %t A188724 ContinuedFraction[t, 120] %Y A188724 Cf. A188640, A188722. %K A188724 nonn,easy,cons %O A188724 1,1 %A A188724 _Clark Kimberling_, Apr 09 2011 %E A188724 a(130) corrected by _Georg Fischer_, Jul 16 2021