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A196825 Decimal expansion of the least x > 0 satisfying 1/(1 + x^2) = sin(x).

%I A196825 #17 Feb 22 2025 19:19:21
%S A196825 7,1,9,4,2,1,2,9,6,3,2,7,4,1,0,3,1,5,7,1,6,9,2,2,9,7,0,0,3,7,3,3,2,0,
%T A196825 4,9,0,8,5,1,0,1,0,6,8,3,9,1,7,9,8,9,7,8,5,7,1,0,4,1,5,7,4,3,2,1,2,3,
%U A196825 5,3,5,3,4,5,8,4,2,0,5,5,0,1,0,8,1,9,4,4,8,3,4,5,2,2,0,3,6,2,2,7
%N A196825 Decimal expansion of the least x > 0 satisfying 1/(1 + x^2) = sin(x).
%H A196825 G. C. Greubel, <a href="/A196825/b196825.txt">Table of n, a(n) for n = 0..10000</a>
%H A196825 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196825 0.7194212963274103157169229700373320490851010...
%t A196825 Plot[{1/(1 + x^2), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, 2}]
%t A196825 t = x /. FindRoot[1 == (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196825 RealDigits[t]  (* A196825 *)
%t A196825 t = x /. FindRoot[1 == 2 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196825 RealDigits[t]  (* A196826 *)
%t A196825 t = x /. FindRoot[1 == 3 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196825 RealDigits[t]  (* A196827 *)
%t A196825 t = x /. FindRoot[1 == 4 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196825 RealDigits[t]  (* A196828 *)
%t A196825 t = x /. FindRoot[1 == 5 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196825 RealDigits[t]  (* A196829 *)
%t A196825 t = x /. FindRoot[1 == 6 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
%t A196825 RealDigits[t]  (* A196830 *)
%o A196825 (PARI) a=1; c=1; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y A196825 Cf. A196832.
%K A196825 nonn,cons
%O A196825 0,1
%A A196825 _Clark Kimberling_, Oct 07 2011