A201735 - OEIS

%I #10 Sep 13 2018 02:55:49

%S 2,0,2,8,4,7,9,6,1,0,6,8,5,8,1,5,7,3,6,5,9,5,8,3,9,4,0,5,8,4,0,7,4,1,

%T 9,6,0,3,3,0,1,0,6,7,3,2,3,1,8,4,9,2,2,9,6,3,9,7,0,7,7,8,1,6,0,4,3,2,

%U 4,8,1,1,9,1,7,0,0,5,7,5,3,8,3,2,3,7,7,0,4,8,3,3,3,7,3,3,6,2,2

%N Decimal expansion of least 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="/A201735/b201735.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, 2.5, 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