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A201582 Decimal expansion of greatest x satisfying x^2 = csc(x) and 0

%I A201582 #12 Feb 07 2025 16:44:07
%S A201582 3,0,3,2,6,4,5,4,1,8,3,8,8,7,5,6,1,8,8,6,7,5,3,2,5,6,3,6,8,0,2,6,0,8,
%T A201582 9,3,2,8,4,6,7,2,3,6,2,6,7,4,9,9,7,1,8,5,9,8,5,1,9,8,4,5,6,7,7,8,0,6,
%U A201582 7,1,1,3,4,1,9,9,2,4,2,2,5,0,4,2,5,5,8,4,3,8,8,9,8,8,9,7,1,0,4
%N A201582 Decimal expansion of greatest x satisfying x^2 = csc(x) and 0<x<Pi.
%C A201582 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201582 G. C. Greubel, <a href="/A201582/b201582.txt">Table of n, a(n) for n = 1..10000</a>
%H A201582 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201582 least:  1.068223544197249018283471114263092898468...
%e A201582 greatest:  3.032645418388756188675325636802608932...
%t A201582 a = 1; c = 0;
%t A201582 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201582 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201582 r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]
%t A201582 RealDigits[r]   (* A196617 *)
%t A201582 r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t A201582 RealDigits[r]   (* A201582 *)
%o A201582 (PARI) a=1; c=0; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018
%Y A201582 Cf. A201564, A196617.
%K A201582 nonn,cons
%O A201582 1,1
%A A201582 _Clark Kimberling_, Dec 03 2011