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A201659 Decimal expansion of greatest x satisfying 9*x^2 = csc(x) and 0 < x < Pi. 3
3, 1, 3, 0, 2, 5, 2, 7, 8, 6, 1, 7, 3, 5, 3, 6, 0, 3, 5, 0, 0, 3, 7, 0, 1, 2, 2, 7, 7, 7, 5, 4, 0, 3, 1, 6, 3, 6, 9, 2, 7, 7, 5, 4, 0, 1, 2, 3, 7, 9, 0, 9, 2, 2, 3, 2, 0, 4, 2, 7, 8, 8, 9, 1, 6, 2, 7, 6, 5, 5, 0, 4, 1, 7, 3, 6, 7, 9, 6, 3, 0, 5, 0, 2, 1, 9, 0, 5, 4, 6, 7, 0, 4, 3, 8, 2, 7, 8, 1 (list; constant; graph; refs; listen; history; text; internal format)
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:  0.4871825725461343607675424300430642207826...

greatest:  3.1302527861735360350037012277754031636...

MATHEMATICA

a = 9; 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, .4, .5}, WorkingPrecision -> 110]

RealDigits[r]    (* A201658 *)

r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]

RealDigits[r]    (* A201659 *)

PROG

(PARI) a=9; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018

CROSSREFS

Cf. A201564.

Sequence in context: A011087 A180021 A091422 * A253625 A244375 A253626

Adjacent sequences:  A201656 A201657 A201658 * A201660 A201661 A201662

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 04 2011

STATUS

approved

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Last modified April 10 11:15 EDT 2021. Contains 342845 sequences. (Running on oeis4.)