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A196819 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=4*cos(x).

%I A196819 #8 Feb 11 2025 13:53:50
%S A196819 1,4,9,3,3,1,9,5,3,5,7,3,8,2,4,2,0,1,9,2,6,6,6,7,6,1,8,4,1,7,9,8,1,8,
%T A196819 4,0,9,6,2,5,3,4,9,9,3,6,9,7,4,1,5,8,7,8,6,6,3,7,2,7,1,3,8,7,3,4,2,0,
%U A196819 8,4,6,1,0,8,8,1,0,1,5,7,6,7,9,2,5,5,0,3,5,7,5,2,7,0,2,8,7,1,1,4
%N A196819 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=4*cos(x).
%H A196819 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196819 1.4933195357382420192666761841798184096253499369741587866...
%t A196819 Plot[{1/(1 + x^2), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, 2}]
%t A196819 t = x /. FindRoot[1 == (1 + x^2) Cos[x], {x, 1, 1.5}, WorkingPrecision -> 100]
%t A196819 RealDigits[t]  (* A196816 *)
%t A196819 t = x /. FindRoot[1 == 2 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196819    WorkingPrecision -> 100]
%t A196819 RealDigits[t]   (* A196817 *)
%t A196819 t = x /. FindRoot[1 == 3 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196819    WorkingPrecision -> 100]
%t A196819 RealDigits[t]  (* A196818 *)
%t A196819 t = x /. FindRoot[1 == 4 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196819    WorkingPrecision -> 100]
%t A196819 RealDigits[t]   (* A196819 *)
%t A196819 t = x /. FindRoot[1 == 5 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196819    WorkingPrecision -> 100]
%t A196819 RealDigits[t]  (* A196820 *)
%t A196819 t = x /. FindRoot[1 == 6 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196819    WorkingPrecision -> 100]
%t A196819 RealDigits[t]  (* A196821 *)
%Y A196819 Cf. A196914.
%K A196819 nonn,cons
%O A196819 1,2
%A A196819 _Clark Kimberling_, Oct 06 2011