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 A188722 #23 Oct 02 2022 22:54:22 %S A188722 3,4,3,2,8,9,2,2,1,5,9,1,3,4,8,3,2,4,4,2,0,1,4,6,0,3,7,0,2,3,5,8,1,0, %T A188722 9,6,6,9,0,2,7,3,4,1,0,5,8,2,0,2,4,4,4,1,9,5,1,0,1,5,2,2,2,1,9,5,8,7, %U A188722 9,8,8,1,1,1,4,5,4,4,9,7,0,2,3,0,4,1,2,0,2,4,6,9,6,5,7,3,3,7,8,4,4,6,2,1,6,9,9,3,2,3,2,9,8,3,6,4,2,4,4,3,3,3,0,0,7,2,7,6,8,8 %N A188722 Decimal expansion of (Pi+sqrt(4+Pi^2))/2. %C A188722 Decimal expansion of shape of a Pi-extension rectangle; see A188640 for definitions of shape and r-extension rectangle. Briefly, an r-extension rectangle is composed of two rectangles having shape r. %C A188722 A Pi-extension rectangle matches the continued fraction A188723 of the shape L/W = (Pi+sqrt(4+Pi^2))/2. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,...]. Specifically, for a Pi-extension rectangle, 3 squares are removed first, then 2 squares, then 3 squares, then 4 squares, then 2 squares,..., so that the original rectangle is partitioned into an infinite collection of squares. %H A188722 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A188722 (Pi+sqrt(4+Pi^2))/2 = [Pi,Pi,Pi,...] (continued fraction). - _Clark Kimberling_, Sep 23 2013 %e A188722 3.4328922159134832442014603702358109669027341058202444195... %t A188722 r = Pi; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] %t A188722 N[t, 130] %t A188722 RealDigits[N[t, 130]][[1]] %t A188722 ContinuedFraction[t, 120] %o A188722 (PARI) (Pi+sqrt(4+Pi^2))/2 \\ _Michel Marcus_, Apr 01 2015 %Y A188722 Cf. A188640, A188723, A188720, A000796. %K A188722 nonn,cons %O A188722 1,1 %A A188722 _Clark Kimberling_, Apr 09 2011