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A196828 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=4*sin(x).

%I A196828 #7 Feb 11 2025 13:55:19
%S A196828 2,3,8,7,7,7,6,5,9,4,4,5,9,0,4,8,5,2,5,6,4,7,2,9,0,3,0,9,5,4,6,1,3,7,
%T A196828 4,7,6,3,8,1,5,3,9,8,9,3,9,2,6,5,3,6,7,9,7,4,7,1,1,8,5,8,5,8,5,8,4,4,
%U A196828 8,3,5,3,5,1,1,3,2,5,0,9,1,9,6,5,3,5,9,0,7,7,4,8,2,0,9,4,5,2,0,4
%N A196828 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=4*sin(x).
%H A196828 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196828 0.238777659445904852564729030954613747638153989...
%t A196828 Plot[{1/(1 + x^2), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, 2}]
%t A196828 t = x /. FindRoot[1 == (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196828 RealDigits[t]  (* A196825 *)
%t A196828 t = x /. FindRoot[1 == 2 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196828 RealDigits[t]  (* A196826 *)
%t A196828 t = x /. FindRoot[1 == 3 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196828 RealDigits[t]  (* A196827 *)
%t A196828 t = x /. FindRoot[1 == 4 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196828 RealDigits[t]  (* A196828 *)
%t A196828 t = x /. FindRoot[1 == 5 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196828 RealDigits[t]  (* A196829 *)
%t A196828 t = x /. FindRoot[1 == 6 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196828 RealDigits[t]  (* A196830 *)
%Y A196828 Cf. A196832.
%K A196828 nonn,cons
%O A196828 0,1
%A A196828 _Clark Kimberling_, Oct 07 2011