A201580 - OEIS

%I #12 Jan 30 2025 13:54:22

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

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

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

%N Decimal expansion of greatest x satisfying x^2 + 9 = 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="/A201580/b201580.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least:  0.111187649530336552411321691800657533611...

%e greatest:  3.087609602783606133001190498846701507...

%t a = 1; c = 9;

%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]   (* A201578 *)

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

%t RealDigits[r]   (* A201580 *)

%o (PARI) a=1; c=9; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018

%Y Cf. A201564.

%K nonn,cons,changed

%O 1,1

%A _Clark Kimberling_, Dec 03 2011