cp's OEIS Frontend

A196914 Decimal expansion of the number c for which the curve y=1/(1+x^2) is tangent to the curve y=c*cos(x), and 0 < x < 2*Pi.

%I A196914 #8 Apr 09 2021 22:46:33
%S A196914 8,7,4,4,6,0,0,3,6,6,2,4,0,0,9,2,6,5,5,4,8,1,4,6,4,4,8,4,0,6,7,3,7,2,
%T A196914 5,6,6,3,0,7,3,9,7,2,6,9,8,4,4,6,9,0,8,1,4,0,1,1,2,0,4,5,2,1,2,5,9,6,
%U A196914 0,1,1,1,5,6,1,3,3,3,0,4,9,8,5,5,8,1,3,8,7,2,6,2,2,4,2,0,7,7,5
%N A196914 Decimal expansion of the number c for which the curve y=1/(1+x^2) is tangent to the curve y=c*cos(x), and 0 < x < 2*Pi.
%F A196914 x=0.87446003662400926554814644840673725663073...
%e A196914 c=0.87446003662400926554814644840673725663073...
%t A196914 Plot[{1/(1 + x^2), 0.874*Cos[x]}, {x, .5, 1}]
%t A196914 t = x /. FindRoot[Tan[x] == 2 x/(1 + x^2), {x, .5, 1}, WorkingPrecision -> 100]
%t A196914 RealDigits[t]    (* A196913 *)
%t A196914 c = N[Sqrt[t^4 + 6 t^2 + 1]/(t^4 + 2 t^2 + 1), 100]
%t A196914 RealDigits[c]    (* A196914 *)
%t A196914 slope = N[-c*Sin[t], 100]
%t A196914 RealDigits[slope](* A196915 *)
%Y A196914 Cf. A196913, A196915.
%K A196914 nonn,cons
%O A196914 0,1
%A A196914 _Clark Kimberling_, Oct 07 2011