A201582 - OEIS

%I #9 Aug 22 2018 05:07:10

%S 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 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 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 Decimal expansion of greatest x satisfying x^2 = 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="/A201582/b201582.txt">Table of n, a(n) for n = 1..10000</a>

%e least:  1.068223544197249018283471114263092898468...

%e greatest:  3.032645418388756188675325636802608932...

%t a = 1; c = 0;

%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, .1, .2}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A196617 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201582 *)

%o (PARI) a=1; c=0; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018

%Y Cf. A201564, A196617.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 03 2011