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A201737 Decimal expansion of least x satisfying x^2 - 4 = csc(x) and 0

%I A201737 #12 Feb 07 2025 16:44:07
%S A201737 2,3,1,5,0,4,6,9,3,3,6,1,7,3,7,4,8,1,7,6,7,1,5,7,6,2,6,2,7,1,9,1,9,4,
%T A201737 3,5,0,8,0,8,1,6,2,2,4,1,0,9,8,6,8,7,3,2,8,6,1,0,7,3,8,5,8,9,6,0,4,4,
%U A201737 1,8,1,1,4,9,2,2,8,2,2,3,1,2,8,4,3,4,1,5,6
%N A201737 Decimal expansion of least x satisfying x^2 - 4 = csc(x) and 0<x<Pi.
%C A201737 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201737 G. C. Greubel, <a href="/A201737/b201737.txt">Table of n, a(n) for n = 1..10000</a>
%H A201737 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201737 least:  2.31504693361737481767157626271919435080...
%e A201737 greatest:  2.91834369901820138765983699207605876...
%t A201737 a = 1; c = -4;
%t A201737 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201737 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201737 r = x /. FindRoot[f[x] == g[x], {x, 2.3, 2.4}, WorkingPrecision -> 110]
%t A201737 RealDigits[r]   (* A201737 *)
%t A201737 r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
%t A201737 RealDigits[r]   (* A201738 *)
%o A201737 (PARI) a=1; c=-4; solve(x=2, 2.5, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018
%Y A201737 Cf. A201564.
%K A201737 nonn,cons
%O A201737 1,1
%A A201737 _Clark Kimberling_, Dec 04 2011