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 A189038 #16 Feb 14 2025 02:04:56 %S A189038 1,6,4,0,3,8,8,2,0,3,2,0,2,2,0,7,5,6,8,7,2,7,6,7,6,2,3,1,9,9,6,7,5,9, %T A189038 6,2,8,1,4,3,3,9,9,9,0,3,1,7,1,7,0,2,5,5,4,2,9,9,8,2,9,1,9,6,6,3,6,8, %U A189038 6,9,2,9,3,2,9,2,2,0,2,6,9,9,1,9,8,4,8,2,9,5,6,3,5,1,3,3,5,5,3,7,0,8,5,5,6,8,0,0,5,1,1,7,4,0,1,7,6,7,7,0,1,9,1,2,6,7,7,6,0,5 %N A189038 Decimal expansion of (9+sqrt(17))/8. %C A189038 Decimal expansion of the shape (= length/width = (9+sqrt(17))/8) of the greater (9/4)-contraction rectangle. %C A189038 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 A189038 This number - 1, namely w = (1 + sqrt(17))/8 = 0.6403882032..., is the positive real root of 4*x^2 - x - 1, with negative root -(-1 + sqrt(17))/8 = -0.3903882032... = -(w - 1/4). - _Wolfdieter Lang_, Dec 12 2022 %e A189038 1.64038820320220756872767623199675962814339990... %t A189038 r = 9/4; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t] %t A189038 N[t, 130] %t A189038 RealDigits[N[t, 130]][[1]] %t A189038 ContinuedFraction[t, 120] %o A189038 (PARI) (sqrt(17)+9)/8 \\ _Charles R Greathouse IV_, Apr 25 2016 %Y A189038 Cf. A188738, A189037. %K A189038 nonn,cons,easy %O A189038 1,2 %A A189038 _Clark Kimberling_, Apr 15 2011