|
%I #11 Sep 13 2018 02:58:12
%S 2,9,9,7,9,9,6,9,2,0,1,8,1,6,9,5,2,6,0,6,6,1,8,2,3,3,3,1,2,5,4,1,2,5,
%T 8,8,7,6,5,4,9,8,3,3,6,8,1,2,0,0,3,2,4,7,4,8,8,3,6,5,9,5,1,9,3,1,0,9,
%U 4,8,3,3,2,2,1,8,8,5,2,1,7,8,8,0,8,7,8,1,3,6,3,4,0,8,0,2,2,7,8
%N Decimal expansion of greatest x satisfying x^2 - 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="/A201683/b201683.txt">Table of n, a(n) for n = 1..10000</a>
%e least: 1.7360324097399950654183110774042852312772...
%e greatest: 2.9979969201816952606618233312541258876...
%t a = 1; c = -2;
%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, 1.7, 1.8}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201682 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201683 *)
%o (PARI) a=1; c=-2; solve(x=2.5, 3, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018
%Y Cf. A201564.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Dec 04 2011
|
