

A201584


Decimal expansion of greatest x satisfying 2*x^2 = csc(x) and 0<x<Pi.


3



3, 0, 8, 9, 1, 7, 4, 2, 1, 1, 9, 2, 9, 9, 3, 0, 2, 0, 6, 5, 6, 0, 5, 7, 7, 4, 8, 7, 8, 6, 9, 9, 7, 3, 8, 0, 4, 9, 3, 7, 1, 6, 3, 0, 9, 6, 5, 6, 6, 7, 2, 1, 0, 0, 2, 6, 5, 8, 0, 5, 8, 8, 2, 2, 6, 9, 1, 1, 0, 0, 8, 9, 9, 1, 3, 2, 5, 0, 5, 1, 6, 3, 6, 1, 8, 4, 8, 9, 4, 4, 8, 0, 0, 1, 6, 6, 3, 6, 6
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OFFSET

1,1


COMMENTS

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


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000


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=3, 3.1, a*x^2 + c  1/sin(x)) \\ G. C. Greubel, Aug 22 2018


CROSSREFS

Cf. A201564.
Sequence in context: A155876 A181977 A199659 * A281298 A095123 A019691
Adjacent sequences: A201581 A201582 A201583 * A201585 A201586 A201587


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Dec 03 2011


STATUS

approved



