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

%I #9 Sep 13 2018 02:55:44

%S 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 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 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 Decimal expansion of greatest x satisfying x^2 - 3 = csc(x) and 0<x<Pi.

%C See A201564 for a guide to related sequences. The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A201736/b201736.txt">Table of n, a(n) for n = 1..10000</a>

%e least: 2.028479610685815736595839405840741960330...

%e greatest: 2.968711981161412446755404392723943506...

%t a = 1; c = -3;

%t f[x_] := a*x^2 + c; g[x_] := Csc[x]

%t Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 2.0, 2.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201735 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201736 *)

%o (PARI) a=1; c=-3; solve(x=2.7, 3, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018

%Y Cf. A201564.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 04 2011

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)