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 A189089 #11 Apr 18 2025 18:07:05 %S A189089 6,1,1,9,7,8,0,7,6,0,6,5,9,1,5,0,0,3,4,4,3,8,4,7,2,6,9,5,5,8,2,9,3,1, %T A189089 2,5,8,9,8,2,6,0,0,1,1,0,4,7,0,8,6,0,0,0,6,0,3,3,3,1,7,3,5,1,4,2,7,1, %U A189089 0,2,0,5,5,3,3,3,7,7,9,4,5,9,9,5,9,0,0,2,0,5,4,1,8,3,2,6,6,4,2,7,5,6,1,2,7,1,2,5,7,9,3,7,1,5,7,8,8,2,5,9,6,6,2,6,5,5,2,7,7,3 %N A189089 Decimal expansion of Pi + sqrt(-1 + Pi^2). %C A189089 Decimal expansion of the shape (= length/width = Pi + sqrt(-1 + Pi^2)) of the greater 2*Pi-contraction rectangle. %C A189089 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. %H A189089 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %e A189089 6.119780760659150034438472695582931258982600110... %t A189089 r = 2*Pi; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t] %t A189089 N[t, 130] %t A189089 RealDigits[N[t, 130]][[1]] (*A189089*) %t A189089 ContinuedFraction[t, 120] (*A189090*) %t A189089 RealDigits[Pi+Sqrt[Pi^2-1],10,150][[1]] (* _Harvey P. Dale_, Apr 18 2025 *) %o A189089 (PARI) Pi + sqrt(Pi^2-1) \\ _Charles R Greathouse IV_, Oct 02 2022 %Y A189089 Cf. A188738, A189090, A189088. %K A189089 nonn,cons %O A189089 1,1 %A A189089 _Clark Kimberling_, Apr 16 2011