A201588 - OEIS

%I #10 Aug 23 2018 02:15:06

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

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

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

%N Decimal expansion of greatest x satisfying 4*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="/A201588/b201588.txt">Table of n, a(n) for n = 1..10000</a>

%e least:  0.6448974755436738344433573900444745201701368...

%e greatest:  3.1158390512762535211310850151952082587811...

%t a = 4; 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, .6, .7}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201587 *)

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

%t RealDigits[r]   (* A201588 *)

%o (PARI) a=4; c=0; solve(x=3.1, 3.14, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018

%Y Cf. A201564.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 03 2011