A201573 - OEIS

%I #12 Nov 11 2018 22:39:24

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

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

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

%N Decimal expansion of greatest x satisfying x^2 + 6 = csc(x) and 0 < x < Pi.

%C See A201564 for a guide to related sequences.  The Mathematica program includes a graph.

%e least:  0.166669163175400949565200320627761299158167...

%e greatest:  3.076894929246192023166693647327725773248...

%t a = 1; c = 6;

%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]   (* A201572 *)

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

%t RealDigits[r]   (* A201573 *)

%o (PARI) a=1; c=6; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018

%Y Cf. A201564.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 03 2011

%E Terms a(87) onward corrected by _G. C. Greubel_, Aug 21 2018