cp's OEIS Frontend

A196774 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.

%I A196774 #9 Apr 09 2021 22:53:36
%S A196774 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 A196774 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 A196774 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 A196774 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 A196774 x=0.4208427526566741951606531250693278249070426065...
%t A196774 Plot[{1/x + .42, Sin[x]}, {x, 0, 2 Pi}]
%t A196774 t = x /. FindRoot[-1 == (x^2) Cos[x], {x, 1.5, 2.5}, WorkingPrecision -> 100]
%t A196774 RealDigits[t]    (* A196773 *)
%t A196774 c = N[-1/t + Sin[t], 100]
%t A196774 RealDigits[c]    (* A196774 *)
%t A196774 slope = N[-1/t^2, 100]
%t A196774 RealDigits[slope](* A196775 *)
%Y A196774 Cf. A196773, A196775.
%K A196774 nonn,cons
%O A196774 0,1
%A A196774 _Clark Kimberling_, Oct 06 2011