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A196817 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=2*cos(x).

%I A196817 #8 Feb 11 2025 13:54:08
%S A196817 1,4,0,1,2,6,9,2,0,7,5,9,9,9,5,7,9,4,2,9,2,7,1,8,7,2,4,3,7,9,0,8,3,4,
%T A196817 1,9,1,5,3,0,8,8,2,8,6,5,4,5,3,3,6,0,2,6,0,3,7,9,1,7,8,2,5,0,7,8,6,3,
%U A196817 1,6,4,0,0,0,4,3,1,7,1,7,3,3,3,7,3,4,8,3,3,1,2,5,9,5,7,5,7,7,9,3
%N A196817 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=2*cos(x).
%H A196817 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196817 x=1.401269207599957942927187243790834191530882865453360260...
%t A196817 Plot[{1/(1 + x^2), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, 2}]
%t A196817 t = x /. FindRoot[1 == (1 + x^2) Cos[x], {x, 1, 1.5}, WorkingPrecision -> 100]
%t A196817 RealDigits[t]  (* A196816 *)
%t A196817 t = x /. FindRoot[1 == 2 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196817    WorkingPrecision -> 100]
%t A196817 RealDigits[t]   (* A196817 *)
%t A196817 t = x /. FindRoot[1 == 3 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196817    WorkingPrecision -> 100]
%t A196817 RealDigits[t]  (* A196818 *)
%t A196817 t = x /. FindRoot[1 == 4 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196817    WorkingPrecision -> 100]
%t A196817 RealDigits[t]   (* A196819 *)
%t A196817 t = x /. FindRoot[1 == 5 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196817    WorkingPrecision -> 100]
%t A196817 RealDigits[t]  (* A196820 *)
%t A196817 t = x /. FindRoot[1 == 6 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196817    WorkingPrecision -> 100]
%t A196817 RealDigits[t]  (* A196821 *)
%Y A196817 Cf. A196914.
%K A196817 nonn,cons
%O A196817 1,2
%A A196817 _Clark Kimberling_, Oct 06 2011