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A201735 Decimal expansion of least x satisfying x^2 - 3 = csc(x) and 0

%I A201735 #13 Feb 07 2025 16:44:07
%S A201735 2,0,2,8,4,7,9,6,1,0,6,8,5,8,1,5,7,3,6,5,9,5,8,3,9,4,0,5,8,4,0,7,4,1,
%T A201735 9,6,0,3,3,0,1,0,6,7,3,2,3,1,8,4,9,2,2,9,6,3,9,7,0,7,7,8,1,6,0,4,3,2,
%U A201735 4,8,1,1,9,1,7,0,0,5,7,5,3,8,3,2,3,7,7,0,4,8,3,3,3,7,3,3,6,2,2
%N A201735 Decimal expansion of least x satisfying x^2 - 3 = csc(x) and 0<x<Pi.
%C A201735 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201735 G. C. Greubel, <a href="/A201735/b201735.txt">Table of n, a(n) for n = 1..10000</a>
%H A201735 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201735 least:  2.028479610685815736595839405840741960330...
%e A201735 greatest:  2.968711981161412446755404392723943506...
%t A201735 a = 1; c = -3;
%t A201735 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201735 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201735 r = x /. FindRoot[f[x] == g[x], {x, 2.0, 2.1}, WorkingPrecision -> 110]
%t A201735 RealDigits[r]   (* A201735 *)
%t A201735 r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
%t A201735 RealDigits[r]   (* A201736 *)
%o A201735 (PARI) a=1; c=-3; solve(x=2, 2.5, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018
%Y A201735 Cf. A201564.
%K A201735 nonn,cons
%O A201735 1,1
%A A201735 _Clark Kimberling_, Dec 04 2011