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A196829 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=5*sin(x).

%I A196829 #9 Feb 11 2025 13:55:15
%S A196829 1,9,3,9,6,2,4,3,0,6,8,1,0,0,6,7,1,6,6,3,0,0,8,0,4,7,1,7,7,3,9,5,7,4,
%T A196829 8,6,5,5,4,8,8,5,3,9,8,6,3,7,7,5,3,2,1,2,5,8,2,5,8,6,8,2,2,0,1,7,3,6,
%U A196829 1,1,6,2,9,7,4,5,9,2,2,6,2,3,1,8,8,6,5,2,8,0,9,3,1,6,2,0,6,3,2,5
%N A196829 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=5*sin(x).
%H A196829 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196829 0.1939624306810067166300804717739574865548853986...
%t A196829 Plot[{1/(1 + x^2), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, 2}]
%t A196829 t = x /. FindRoot[1 == (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196829 RealDigits[t]  (* A196825 *)
%t A196829 t = x /. FindRoot[1 == 2 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196829 RealDigits[t]  (* A196826 *)
%t A196829 t = x /. FindRoot[1 == 3 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196829 RealDigits[t]  (* A196827 *)
%t A196829 t = x /. FindRoot[1 == 4 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196829 RealDigits[t]  (* A196828 *)
%t A196829 t = x /. FindRoot[1 == 5 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196829 RealDigits[t]  (* A196829 *)
%t A196829 t = x /. FindRoot[1 == 6 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196829 RealDigits[t]  (* A196830 *)
%Y A196829 Cf. A196832.
%K A196829 nonn,cons
%O A196829 0,2
%A A196829 _Clark Kimberling_, Oct 07 2011
%E A196829 Offset corrected by _Georg Fischer_, Aug 10 2021