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 A188636 #16 Oct 20 2024 00:27:19 %S A188636 2,7,7,4,6,2,2,8,9,9,5,0,4,4,8,9,2,6,3,1,9,8,2,4,9,6,3,7,9,1,9,4,7,7, %T A188636 5,5,4,6,6,5,5,1,0,3,3,6,5,2,8,2,0,8,1,8,7,3,4,9,5,1,3,3,9,2,9,6,5,9, %U A188636 8,4,1,0,4,5,2,8,3,9,2,6,6,1,8,6,4,7,1,2,8,2,0,8,9,9,5,0,5,2,0,5,9,6,5,7,2,1,2,9,0,9,4,9,2,5,1,3,9,0,2,4,7,6,0,8,3,9,2,3,0,9 %N A188636 Decimal expansion of length/width of a metasilver rectangle. %C A188636 A metasilver rectangle is introduced here as a rectangle such that if a silver rectangle is removed from one end, the remaining rectangle is metasilver. Recall that a rectangle is silver if the removal of 2 squares from one end leaves a rectangle having the same shape s=(length/width) as the original. This metasilver ratio is given by %C A188636 s=2.774622899504489263198249637919477554666...; %C A188636 s=[r,r,r,r...], a periodic continued fraction, r=1+sqrt(2); %C A188636 s=[2,1,3,2,3,2,7,1,1,114,11,1,2,1,...], as at A188637. %H A188636 Clark Kimberling, <a href="http://www.jstor.org/stable/27963362">A Visual Euclidean Algorithm</a>, The Mathematics Teacher 76 (1983) 108-109. %F A188636 Equals (1+sqrt(2)+sqrt(H))/2, where H=7+2*sqrt(2). %t A188636 t=1+2^(1/2); r=(t+(t^2+4)^(1/2))/2 %t A188636 FullSimplify[r] %t A188636 N[r, 130] %t A188636 RealDigits[N[r, 130]][[1]] %Y A188636 Cf. A188637, A136319, A188635, A188638, A188639. %K A188636 nonn,cons,easy %O A188636 1,1 %A A188636 _Clark Kimberling_, Apr 06 2011