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A196826 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=2*sin(x).

%I A196826 #9 Feb 11 2025 13:55:23
%S A196826 4,3,4,2,0,2,5,4,9,9,9,8,1,9,6,3,8,6,8,1,3,5,2,4,4,2,1,9,6,6,6,8,4,0,
%T A196826 1,9,8,3,9,6,2,3,8,0,7,6,4,7,6,7,2,5,5,4,6,4,7,2,0,6,3,4,8,5,3,3,2,3,
%U A196826 7,1,0,7,3,3,7,0,0,8,1,7,2,0,8,8,0,7,6,7,5,2,2,1,5,6,0,7,5,5,5,4
%N A196826 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=2*sin(x).
%H A196826 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196826 0.43420254999819638681352442196668401983962380...
%t A196826 Plot[{1/(1 + x^2), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, 2}]
%t A196826 t = x /. FindRoot[1 == (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196826 RealDigits[t]  (* A196825 *)
%t A196826 t = x /. FindRoot[1 == 2 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196826 RealDigits[t]  (* A196826 *)
%t A196826 t = x /. FindRoot[1 == 3 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196826 RealDigits[t]  (* A196827 *)
%t A196826 t = x /. FindRoot[1 == 4 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196826 RealDigits[t]  (* A196828 *)
%t A196826 t = x /. FindRoot[1 == 5 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196826 RealDigits[t]  (* A196829 *)
%t A196826 t = x /. FindRoot[1 == 6 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196826 RealDigits[t]  (* A196830 *)
%Y A196826 Cf. A196832.
%K A196826 nonn,cons
%O A196826 0,1
%A A196826 _Clark Kimberling_, Oct 07 2011