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A201736 Decimal expansion of greatest x satisfying x^2 - 3 = csc(x) and 0

%I A201736 #12 Feb 07 2025 16:44:07
%S A201736 2,9,6,8,7,1,1,9,8,1,1,6,1,4,1,2,4,4,6,7,5,5,4,0,4,3,9,2,7,2,3,9,4,3,
%T A201736 5,0,6,7,7,5,0,7,0,0,7,7,8,9,2,3,2,6,2,9,2,3,9,0,3,1,2,1,2,3,6,6,6,1,
%U A201736 0,5,9,8,6,6,3,4,1,4,8,9,1,2,6,0,8,0,6,5,8,5,6,2,5,1,6,6,4,7,0
%N A201736 Decimal expansion of greatest x satisfying x^2 - 3 = csc(x) and 0<x<Pi.
%C A201736 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201736 G. C. Greubel, <a href="/A201736/b201736.txt">Table of n, a(n) for n = 1..10000</a>
%H A201736 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201736 least:  2.028479610685815736595839405840741960330...
%e A201736 greatest:  2.968711981161412446755404392723943506...
%t A201736 a = 1; c = -3;
%t A201736 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201736 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201736 r = x /. FindRoot[f[x] == g[x], {x, 2.0, 2.1}, WorkingPrecision -> 110]
%t A201736 RealDigits[r]   (* A201735 *)
%t A201736 r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
%t A201736 RealDigits[r]   (* A201736 *)
%o A201736 (PARI) a=1; c=-3; solve(x=2.7, 3, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018
%Y A201736 Cf. A201564.
%K A201736 nonn,cons
%O A201736 1,1
%A A201736 _Clark Kimberling_, Dec 04 2011