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A196820 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=5*cos(x).

%I A196820 #8 Feb 11 2025 13:54:24
%S A196820 1,5,0,9,7,7,1,9,0,0,4,7,0,7,2,6,8,8,5,3,5,5,4,9,3,7,5,3,5,0,0,9,8,6,
%T A196820 5,9,9,4,4,8,6,3,7,7,2,7,5,6,3,8,3,7,3,0,5,0,6,6,8,0,5,9,3,4,3,1,5,3,
%U A196820 7,5,3,9,5,9,0,0,9,7,0,3,7,1,1,0,9,2,9,0,8,1,2,9,7,3,8,7,9,0,2,1
%N A196820 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=5*cos(x).
%H A196820 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196820 1.50977190047072688535549375350098659944863772756...
%t A196820 Plot[{1/(1 + x^2), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, 2}]
%t A196820 t = x /. FindRoot[1 == (1 + x^2) Cos[x], {x, 1, 1.5}, WorkingPrecision -> 100]
%t A196820 RealDigits[t]  (* A196816 *)
%t A196820 t = x /. FindRoot[1 == 2 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196820    WorkingPrecision -> 100]
%t A196820 RealDigits[t]   (* A196817 *)
%t A196820 t = x /. FindRoot[1 == 3 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196820    WorkingPrecision -> 100]
%t A196820 RealDigits[t]  (* A196818 *)
%t A196820 t = x /. FindRoot[1 == 4 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196820    WorkingPrecision -> 100]
%t A196820 RealDigits[t]   (* A196819 *)
%t A196820 t = x /. FindRoot[1 == 5 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196820    WorkingPrecision -> 100]
%t A196820 RealDigits[t]  (* A196820 *)
%t A196820 t = x /. FindRoot[1 == 6 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196820    WorkingPrecision -> 100]
%t A196820 RealDigits[t]  (* A196821 *)
%Y A196820 Cf. A196914.
%K A196820 nonn,cons
%O A196820 1,2
%A A196820 _Clark Kimberling_, Oct 06 2011