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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 (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: 0.875943738724356441549462867955303876323370...

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

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Last modified November 27 01:14 EST 2022. Contains 358362 sequences. (Running on oeis4.)