A201568 - OEIS

%I #10 Aug 22 2018 08:30:01

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

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

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

%N Decimal expansion of least x satisfying x^2 + 4 = 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="/A201568/b201568.txt">Table of n, a(n) for n = 0..10000</a>

%e least:  0.2487490007162959853652924083716941039...

%e greatest:  3.0669301776557967159210627137381980...

%t a = 1; c = 4;

%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, .2, .3}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201568 *)

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

%t RealDigits[r]   (* A201569 *)

%o (PARI) a=1; c=4; solve(x=0.2, .3, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018

%Y Cf. A201564.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 03 2011