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 A196832 #11 Feb 22 2025 19:24:34
%S A196832 2,1,1,7,5,2,6,7,2,8,4,3,1,3,3,5,6,4,2,2,8,9,1,8,2,8,8,7,8,3,0,2,6,3,
%T A196832 7,0,7,8,1,5,9,5,1,6,7,9,1,0,4,6,3,2,3,2,6,2,5,2,5,9,6,1,4,0,8,2,5,0,
%U A196832 7,4,4,7,1,8,8,9,8,5,5,0,0,4,1,4,6,5,1,6,9,1,0,2,3,3,1,7,2,8,0,9
%N A196832 Decimal expansion of the number c for which the curve y=1/(1+x^2) is tangent to the curve y=c*sin(x), and 0 < x < 2*Pi.
%e A196832 c=0.21175267284313356422891828878302637078159516791...
%t A196832 Plot[{1/(1 + x^2), .205 Sin[x]}, {x, 0, Pi}]
%t A196832 t = x /. FindRoot[x^2 + 2 x*Tan[x] + 1 == 0, {x, 2, 3}, WorkingPrecision -> 100]
%t A196832 RealDigits[t] (* A196831 *)
%t A196832 c = N[Csc[t]/(1 + t^2), 100]
%t A196832 RealDigits[c] (* A196832 *)
%t A196832 slope = N[c*Cos[t], 100]
%t A196832 RealDigits[slope] (* A196833 *)
%o A196832 (PARI) t=solve(x=2,3, x^2 + 2*x*tan(x) + 1); 1/sin(t)/(1 + t^2) \\ _Charles R Greathouse IV_, Feb 22 2025
%Y A196832 Cf. A196825.
%K A196832 nonn,cons
%O A196832 0,1
%A A196832 _Clark Kimberling_, Oct 07 2011