A196759 - OEIS

%I #10 Mar 06 2021 01:55:33

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

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

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

%N Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/x and y=c*sin(x), where c is given by A196758.

%e x=-0.242962685095034086912611580795123073012...

%t Plot[{1/x, .55*Sin[x]}, {x, 0, Pi}]

%t xt = x /. FindRoot[x + Tan[x] == 0, {x, 1.5, 2.5}, WorkingPrecision -> 100]

%t RealDigits[xt] (* A196504 *)

%t c = N[1/(xt*Sin[xt]), 100]

%t RealDigits[c]  (* A196758 *)

%t slope = -1/xt^2

%t RealDigits[slope]  (* A196759 *)

%Y Cf. A196758.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 06 2011