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 A188943 #13 Aug 30 2022 14:09:51 %S A188943 1,7,6,7,5,9,1,8,7,9,2,4,3,9,9,8,2,1,5,5,1,9,8,7,0,2,1,1,2,4,5,0,8,2, %T A188943 6,5,7,7,0,8,5,4,9,4,2,8,9,7,4,2,0,7,7,0,2,1,1,8,4,0,8,8,4,2,7,0,4,5, %U A188943 2,7,8,2,4,7,1,5,5,0,1,7,4,0,8,6,7,4,3,6,5,1,3,6,6,9,7,4,8,4,5,2,9,4,5,5,8,5,6,9,7,0,0,4,0,1,0,5,9,0,0,6,2,6,7,1,7,7,9,7,1,0 %N A188943 Decimal expansion of (7 + sqrt(13))/6. %C A188943 Decimal expansion of the shape (= length/width = (7+sqrt(13))/6) of the greater (7/3)-contraction rectangle. %C A188943 See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes. %C A188943 From _Wolfdieter Lang_, Aug 29 2022: (Start) %C A188943 This constant t is an element of the quadratic number field Q(sqrt(13)) with (monic) polynomial x^2 - (7/3)*x + 1, and the negative root is -A188942. %C A188943 The constant t - 1 = (1 + sqrt(13))/6 = A209927/3 has minimal polynomial x^2 - x/3 - 1/3, with negative root -(-1 + sqrt(13))/6 = -A223139/3 = -A356033. %C A188943 (End) %e A188943 1.7675918792439982155198702112450826577085494289742... %t A188943 r = 7/3; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t] %t A188943 N[t, 130] %t A188943 RealDigits[N[t, 130]][[1]] %t A188943 ContinuedFraction[t, 120] %Y A188943 Cf. A188738, A188942, A209927, A223139, A356033. %K A188943 nonn,cons %O A188943 1,2 %A A188943 _Clark Kimberling_, Apr 14 2011