cp's OEIS Frontend

A201585 Decimal expansion of least x satisfying 3*x^2 = csc(x) and 0

%I A201585 #12 Feb 07 2025 16:44:07
%S A201585 7,1,3,6,1,1,5,4,1,0,6,5,4,5,3,5,1,6,9,6,7,1,2,3,4,8,7,4,8,4,8,2,8,2,
%T A201585 3,1,1,4,4,0,0,5,5,5,1,9,8,5,0,0,2,7,5,7,8,8,6,3,6,5,8,4,1,9,1,4,4,4,
%U A201585 9,9,0,3,5,1,3,2,8,5,5,6,4,8,4,8,0,8,7,8,7,0,0,2,5,8,9,6,5,5,0
%N A201585 Decimal expansion of least x satisfying 3*x^2 = csc(x) and 0<x<Pi.
%C A201585 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201585 G. C. Greubel, <a href="/A201585/b201585.txt">Table of n, a(n) for n = 0..10000</a>
%H A201585 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201585 least:  0.71361154106545351696712348748482823114400555...
%e A201585 greatest:  3.10705708466927913942133639758902326551860...
%t A201585 a = 3; c = 0;
%t A201585 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201585 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201585 r = x /. FindRoot[f[x] == g[x], {x, .7, .8}, WorkingPrecision -> 110]
%t A201585 RealDigits[r]    (* A201585 *)
%t A201585 r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
%t A201585 RealDigits[r]    (* A201586 *)
%o A201585 (PARI) a=3; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018
%Y A201585 Cf. A201564.
%K A201585 nonn,cons
%O A201585 0,1
%A A201585 _Clark Kimberling_, Dec 03 2011