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%I #9 Apr 09 2021 22:53:36
%S 4,2,0,8,4,2,7,5,2,6,5,6,6,7,4,1,9,5,1,6,0,6,5,3,1,2,5,0,6,9,3,2,7,8,
%T 2,4,9,0,7,0,4,2,6,0,6,5,4,9,7,3,8,9,8,9,0,5,0,2,0,0,6,4,2,0,9,6,9,4,
%U 9,8,0,6,5,0,6,4,7,9,2,4,4,8,6,7,5,2,7,9,8,5,5,9,2,8,9,1,2,3,1
%N Decimal expansion of the number c for which the curve y=c+1/x is tangent to the curve y=sin(x), and 0 < x < 2*Pi.
%e x=0.4208427526566741951606531250693278249070426065...
%t Plot[{1/x + .42, Sin[x]}, {x, 0, 2 Pi}]
%t t = x /. FindRoot[-1 == (x^2) Cos[x], {x, 1.5, 2.5}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196773 *)
%t c = N[-1/t + Sin[t], 100]
%t RealDigits[c] (* A196774 *)
%t slope = N[-1/t^2, 100]
%t RealDigits[slope](* A196775 *)
%Y Cf. A196773, A196775.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 06 2011
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