A201574 - OEIS

%I #10 Aug 22 2018 08:29:16

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

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

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

%N Decimal expansion of least x satisfying x^2 + 7 = 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="/A201574/b201574.txt">Table of n, a(n) for n = 0..10000</a>

%e least:  0.14292758299392086700431044307554748240884...

%e greatest:  3.08092023229520680455935849821275370108...

%t a = 1; c = 7;

%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]   (* A201574 *)

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

%t RealDigits[r]   (* A201575 *)

%o (PARI) a=1; c=7; solve(x=0.1, .2, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018

%Y Cf. A201564.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Dec 03 2011