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 A188883 #10 Oct 01 2022 14:09:04 %S A188883 1,3,6,7,7,4,8,3,9,4,9,3,1,3,6,7,4,4,4,6,9,9,6,9,1,7,6,5,6,8,2,2,0,5, %T A188883 4,5,5,6,5,1,1,1,3,2,6,8,9,0,2,1,4,8,8,6,9,4,7,5,0,0,4,6,5,7,5,6,7,1, %U A188883 5,3,4,5,6,2,8,2,0,1,7,6,9,3,0,7,9,0,1,9,3,0,9,7,4,1,9,3,2,3,3,5,3,1,2,2,6,6,3,0,2,7,3,4,3,3,0,8,1,4,5,9,8,2,2,8,1,5,8,9,1,9 %N A188883 Decimal expansion of (1 + sqrt(1 + Pi^2))/Pi. %C A188883 Decimal expansion of the length/width ratio of a (2/Pi)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle. %C A188883 A (2/Pi)-extension rectangle matches the continued fraction [1,2,1,2,1,1,3,1,1,5,1,7,1,1,23,2,...] for the shape L/W = (1 + sqrt(1 + Pi^2))/Pi. 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 (2/Pi)-extension rectangle, 1 square is removed first, then 2 squares, then 1 square, then 2 squares, ..., so that the original rectangle of shape (1 + sqrt(1 + Pi^2))/Pi is partitioned into an infinite collection of squares. %H A188883 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %e A188883 1.36774839493136744469969176568220545565111326890... %t A188883 r = 2/Pi; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] %t A188883 N[t, 130] %t A188883 RealDigits[N[t, 130]][[1]] %t A188883 ContinuedFraction[t, 120] %o A188883 (PARI) (sqrt(Pi^2+1)+1)/Pi \\ _Charles R Greathouse IV_, Oct 01 2022 %Y A188883 Cf. A188640, A188884, A188724, A188726. %K A188883 nonn,cons %O A188883 1,2 %A A188883 _Clark Kimberling_, Apr 12 2011