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A196827 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=3*sin(x).

%I A196827 #7 Feb 11 2025 13:55:21
%S A196827 3,0,9,1,5,4,9,3,3,5,5,8,9,7,2,5,7,9,2,5,2,5,3,4,5,2,4,1,8,9,6,4,0,4,
%T A196827 3,0,0,8,1,3,4,9,4,2,0,3,9,0,9,1,3,3,7,3,7,4,3,3,9,3,4,6,8,0,0,7,1,1,
%U A196827 5,8,5,1,4,2,9,6,6,0,2,9,9,9,9,3,2,8,9,6,2,5,5,0,5,3,4,7,8,9,4,5
%N A196827 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=3*sin(x).
%H A196827 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196827 0.3091549335589725792525345241896404300813494203...
%t A196827 Plot[{1/(1 + x^2), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, 2}]
%t A196827 t = x /. FindRoot[1 == (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196827 RealDigits[t]  (* A196825 *)
%t A196827 t = x /. FindRoot[1 == 2 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196827 RealDigits[t]  (* A196826 *)
%t A196827 t = x /. FindRoot[1 == 3 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196827 RealDigits[t]  (* A196827 *)
%t A196827 t = x /. FindRoot[1 == 4 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196827 RealDigits[t]  (* A196828 *)
%t A196827 t = x /. FindRoot[1 == 5 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196827 RealDigits[t]  (* A196829 *)
%t A196827 t = x /. FindRoot[1 == 6 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196827 RealDigits[t]  (* A196830 *)
%Y A196827 Cf. A196832.
%K A196827 nonn,cons
%O A196827 0,1
%A A196827 _Clark Kimberling_, Oct 07 2011