

A201667


Decimal expansion of greatest x satisfying 3*x^2  1 = csc(x) and 0<x<Pi.


3



3, 1, 0, 5, 7, 9, 1, 2, 2, 9, 3, 6, 3, 0, 8, 2, 2, 7, 7, 9, 2, 8, 9, 6, 7, 9, 3, 1, 6, 1, 4, 3, 1, 4, 3, 0, 3, 5, 9, 5, 3, 6, 9, 7, 6, 5, 5, 5, 2, 9, 1, 7, 0, 3, 3, 2, 2, 8, 1, 2, 7, 8, 5, 1, 1, 4, 2, 9, 5, 2, 0, 6, 7, 4, 2, 4, 0, 0, 2, 7, 5, 4, 0, 8, 2, 0, 1, 2, 1, 2, 0, 0, 3, 9, 9, 4, 5, 3, 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: 0.875943738724356441549462867955303876323370...
greatest: 3.105791229363082277928967931614314303595...


MATHEMATICA

a = 3; c = 1;
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] (* A201666 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision > 110]
RealDigits[r] (* A201667 *)


PROG

(PARI) a=3; c=1; solve(x=3, 3.14, a*x^2 + c  1/sin(x)) \\ G. C. Greubel, Sep 11 2018


CROSSREFS

Cf. A201564.
Sequence in context: A227342 A329989 A110032 * A175779 A280819 A300280
Adjacent sequences: A201664 A201665 A201666 * A201668 A201669 A201670


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Dec 04 2011


STATUS

approved



