A201659 - OEIS

%I #9 Sep 12 2018 01:32:57

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

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

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

%N Decimal expansion of greatest x satisfying 9*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="/A201659/b201659.txt">Table of n, a(n) for n = 1..10000</a>

%e least:  0.4871825725461343607675424300430642207826...

%e greatest:  3.1302527861735360350037012277754031636...

%t a = 9; 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, .4, .5}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201658 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201659 *)

%o (PARI) a=9; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 11 2018

%Y Cf. A201564.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 04 2011