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A196821 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=6*cos(x).

%I A196821 #8 Feb 11 2025 13:55:26
%S A196821 1,5,2,0,4,4,9,4,5,0,8,3,3,8,1,6,3,6,3,1,4,7,4,5,8,8,2,0,8,9,0,5,6,3,
%T A196821 9,6,3,1,3,8,9,8,5,3,0,5,5,8,3,2,7,8,4,3,5,1,8,1,2,8,9,3,4,0,1,3,6,8,
%U A196821 8,1,5,5,1,6,1,1,3,2,8,2,2,3,1,6,8,8,9,2,6,3,2,4,0,2,9,2,6,1,3,9
%N A196821 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=6*cos(x).
%H A196821 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196821 1.5204494508338163631474588208905639631389853055832784...
%t A196821 Plot[{1/(1 + x^2), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, 2}]
%t A196821 t = x /. FindRoot[1 == (1 + x^2) Cos[x], {x, 1, 1.5}, WorkingPrecision -> 100]
%t A196821 RealDigits[t]  (* A196816 *)
%t A196821 t = x /. FindRoot[1 == 2 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196821    WorkingPrecision -> 100]
%t A196821 RealDigits[t]   (* A196817 *)
%t A196821 t = x /. FindRoot[1 == 3 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196821    WorkingPrecision -> 100]
%t A196821 RealDigits[t]  (* A196818 *)
%t A196821 t = x /. FindRoot[1 == 4 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196821    WorkingPrecision -> 100]
%t A196821 RealDigits[t]   (* A196819 *)
%t A196821 t = x /. FindRoot[1 == 5 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196821    WorkingPrecision -> 100]
%t A196821 RealDigits[t]  (* A196820 *)
%t A196821 t = x /. FindRoot[1 == 6 (1 + x^2) Cos[x], {x, 1, 1.6},
%t A196821    WorkingPrecision -> 100]
%t A196821 RealDigits[t]  (* A196821 *)
%Y A196821 Cf. A196914.
%K A196821 nonn,cons
%O A196821 1,2
%A A196821 _Clark Kimberling_, Oct 06 2011