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 A188735 #13 Sep 08 2022 08:45:56 %S A188735 4,7,1,2,2,1,4,4,5,0,4,4,9,0,2,6,1,8,0,4,3,6,5,5,2,8,5,3,7,2,9,4,0,6, %T A188735 1,2,0,4,2,4,0,3,4,0,7,1,8,6,0,6,9,1,0,4,2,9,3,0,7,8,8,6,3,2,4,5,9,1, %U A188735 1,0,1,4,5,9,2,6,9,1,9,6,5,7,5,2,3,3,0,0,1,9,6,0,2,8,8,5,6,4,4,0,6,0,9,5,2,5,2,9,9,7,1,7,9,3,7,2,9,9,9,2,9,5,1,8,7,7,5,9,3,4 %N A188735 Decimal expansion of (9+sqrt(97))/4. %C A188735 Decimal expansion of the length/width ratio of a (9/2)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle. %C A188735 A (9/2)-extension rectangle matches the continued fraction [4,1,2,2,9,2,2,1,4,4,1,2,2,9,...] for the shape L/W=(9+sqrt(97))/4. 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 (9/2)-extension rectangle, 4 squares are removed first, then 1 square, then 2 squares, then 2 squares,..., so that the original rectangle of shape (9+sqrt(97))/4 is partitioned into an infinite collection of squares. %H A188735 G. C. Greubel, <a href="/A188735/b188735.txt">Table of n, a(n) for n = 1..10000</a> %e A188735 4.712214450449026180436552853729406120424034071860691042930... %p A188735 evalf((9+sqrt(97))/4,140); # _Muniru A Asiru_, Nov 01 2018 %t A188735 r = 9/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] %t A188735 N[t, 130] %t A188735 RealDigits[N[t, 130]][[1]] %t A188735 ContinuedFraction[t, 120] %o A188735 (PARI) (sqrt(97)+9)/4 \\ _Charles R Greathouse IV_, Apr 25 2016 %o A188735 (Magma) SetDefaultRealField(RealField(100)); (9+Sqrt(97))/4; // _G. C. Greubel_, Nov 01 2018 %Y A188735 Cf. A188640, A188734. %K A188735 nonn,cons %O A188735 1,1 %A A188735 _Clark Kimberling_, Apr 12 2011