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%I #8 Apr 09 2021 16:12:01
%S 2,2,1,4,4,1,6,9,0,5,0,7,9,6,3,6,3,3,0,6,7,9,5,6,5,9,6,0,3,6,7,7,9,2,
%T 2,1,5,9,6,6,3,7,6,4,7,5,4,4,0,5,8,6,1,5,8,1,4,8,7,3,1,8,2,5,7,6,3,1,
%U 6,5,9,4,0,8,0,2,1,0,6,1,9,9,6,1,9,3,4,3,0,3,0,7,2,8,3,6,9,2,7,0
%N Decimal expansion of the number x satisfying 0 < x < 2*Pi and x^2 + 2*x*tan(x) + 1 = 0.
%e x=2.214416905079636330679565960367792215966376475...
%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 1,1
%A _Clark Kimberling_, Oct 07 2011
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