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A201583
Decimal expansion of least x satisfying 2*x^2 = csc(x) and 0<x<Pi.
3
8, 2, 5, 0, 2, 8, 9, 2, 4, 0, 1, 5, 0, 0, 6, 3, 3, 9, 3, 3, 3, 9, 4, 6, 3, 1, 8, 1, 8, 3, 3, 5, 7, 9, 7, 8, 6, 9, 2, 2, 8, 7, 1, 0, 1, 4, 8, 2, 8, 7, 1, 0, 8, 8, 5, 2, 7, 4, 2, 5, 2, 0, 4, 2, 7, 7, 8, 5, 7, 4, 3, 9, 1, 0, 4, 3, 1, 4, 1, 6, 8, 3, 6, 0, 1, 4, 4, 0, 9, 8, 7, 0, 3, 4, 7, 3, 9, 6, 2
OFFSET
0,1
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.825028924015006339333946318183357978692...
greatest: 3.089174211929930206560577487869973804...
MATHEMATICA
a = 2; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]
RealDigits[r] (* A201583 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r] (* A201584 *)
PROG
(PARI) a=2; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018
CROSSREFS
Cf. A201564.
Sequence in context: A109614 A248301 A284157 * A243370 A179048 A173158
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 03 2011
STATUS
approved