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A196818 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=3*cos(x).

%I A196818 #10 Feb 11 2025 13:54:04
%S A196818 1,4,6,4,6,1,1,4,7,9,7,0,1,4,2,5,0,0,5,0,1,4,6,4,8,0,4,8,0,1,0,0,2,5,
%T A196818 9,9,7,8,1,8,0,8,4,8,1,3,1,0,9,6,2,6,9,6,0,3,7,9,0,7,1,1,0,1,7,5,5,7,
%U A196818 2,5,3,9,2,4,2,6,1,6,4,8,4,7,8,7,8,4,3,0,1,6,9,7,9,9,2,0,1,0,2,6,8,5
%N A196818 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=3*cos(x).
%H A196818 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196818 1.46461147970142500501464804801002599781808481310...
%t A196818 Plot[{1/(1 + x^2), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, 2}]
%t A196818 t = x /. FindRoot[1 == (1 + x^2) Cos[x], {x, 1, 1.5}, WorkingPrecision -> 100]
%t A196818 RealDigits[t]  (* A196816 *)
%t A196818 t = x /. FindRoot[1 == 2 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196818    WorkingPrecision -> 100]
%t A196818 RealDigits[t]   (* A196817 *)
%t A196818 t = x /. FindRoot[1 == 3 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196818    WorkingPrecision -> 100]
%t A196818 RealDigits[t]  (* A196818 *)
%t A196818 t = x /. FindRoot[1 == 4 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196818    WorkingPrecision -> 100]
%t A196818 RealDigits[t]   (* A196819 *)
%t A196818 t = x /. FindRoot[1 == 5 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196818    WorkingPrecision -> 100]
%t A196818 RealDigits[t]  (* A196820 *)
%t A196818 t = x /. FindRoot[1 == 6 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196818    WorkingPrecision -> 100]
%t A196818 RealDigits[t]  (* A196821 *)
%Y A196818 Cf. A196914.
%K A196818 nonn,cons
%O A196818 1,2
%A A196818 _Clark Kimberling_, Oct 06 2011