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A201736 Decimal expansion of greatest x satisfying x^2 - 3 = csc(x) and 0<x<Pi. 3
2, 9, 6, 8, 7, 1, 1, 9, 8, 1, 1, 6, 1, 4, 1, 2, 4, 4, 6, 7, 5, 5, 4, 0, 4, 3, 9, 2, 7, 2, 3, 9, 4, 3, 5, 0, 6, 7, 7, 5, 0, 7, 0, 0, 7, 7, 8, 9, 2, 3, 2, 6, 2, 9, 2, 3, 9, 0, 3, 1, 2, 1, 2, 3, 6, 6, 6, 1, 0, 5, 9, 8, 6, 6, 3, 4, 1, 4, 8, 9, 1, 2, 6, 0, 8, 0, 6, 5, 8, 5, 6, 2, 5, 1, 6, 6, 4, 7, 0 (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:  2.028479610685815736595839405840741960330...

greatest:  2.968711981161412446755404392723943506...

MATHEMATICA

a = 1; c = -3;

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, 2.0, 2.1}, WorkingPrecision -> 110]

RealDigits[r]   (* A201735 *)

r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]

RealDigits[r]   (* A201736 *)

PROG

(PARI) a=1; c=-3; solve(x=2.7, 3, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018

CROSSREFS

Cf. A201564.

Sequence in context: A233766 A021341 A011247 * A068632 A320037 A122664

Adjacent sequences:  A201733 A201734 A201735 * A201737 A201738 A201739

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 04 2011

STATUS

approved

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Last modified May 24 00:38 EDT 2019. Contains 323528 sequences. (Running on oeis4.)