A196833 - OEIS

%I #9 Mar 06 2021 02:01:59

%S 1,2,7,0,7,1,8,4,1,1,8,6,4,4,1,9,0,5,9,4,7,9,4,4,6,4,3,3,9,3,0,0,1,7,

%T 6,8,3,8,5,6,2,5,4,4,7,1,6,6,1,6,1,6,3,2,0,7,5,0,6,4,5,8,1,2,0,3,8,7,

%U 5,4,2,8,7,7,9,2,4,1,7,9,1,2,7,7,0,9,9,2,3,3,8,2,7,6,7,3,3,4,3,7

%N Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*sin(x), where c is given by A196832.

%e x=-0.12707184118644190594794464339300176838562544...

%t Plot[{1/(1 + x^2), .205 Sin[x]}, {x, 0, Pi}]

%t t = x /. FindRoot[x^2 + 2 x*Tan[x] + 1 == 0, {x, 2, 3}, WorkingPrecision -> 100]

%t RealDigits[t]     (* A196831 *)

%t c = N[Csc[t]/(1 + t^2), 100]

%t RealDigits[c]     (* A196832 *)

%t slope = N[c*Cos[t], 100]

%t RealDigits[slope] (* A196833 *)

%Y Cf. A196825, A196832.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Oct 07 2011