A201679 - OEIS

%I #12 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of greatest x satisfying 9*x^2 - 1 = 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="/A201679/b201679.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:  0.5645945233946045603454170508793526321622...

%e greatest:  3.1301217443279103173861938064228046468...

%t a = 9; c = -1;

%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, .5, .6}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201678 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201679 *)

%o (PARI) a=9; c=-1; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018

%Y Cf. A201564.

%K nonn,cons,changed

%O 1,1

%A _Clark Kimberling_, Dec 04 2011