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A201567 Decimal expansion of greatest x satisfying x^2 + 3 = csc(x) and 0 < x < Pi. 3
3, 0, 6, 0, 6, 4, 7, 6, 2, 1, 6, 7, 4, 3, 9, 0, 6, 4, 9, 4, 6, 7, 0, 2, 1, 0, 6, 1, 4, 4, 1, 5, 7, 5, 3, 7, 2, 7, 8, 8, 8, 9, 0, 1, 2, 3, 3, 7, 6, 9, 2, 2, 2, 7, 4, 3, 9, 7, 9, 9, 5, 2, 3, 0, 0, 1, 8, 8, 1, 8, 3, 7, 3, 7, 3, 6, 9, 0, 6, 0, 9, 4, 1, 8, 6, 6, 2, 9, 2, 4, 4, 0, 1, 7, 3, 8, 0, 7, 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:  0.3276482471136686780982477062098195298...

greatest:  3.0606476216743906494670210614415753...

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, .3, .4}, WorkingPrecision -> 110]

RealDigits[r]    (* A201567 *)

r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]

RealDigits[r]   (* A201568 *)

PROG

(PARI) a=1; c=3; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

CROSSREFS

Cf. A201564.

Sequence in context: A321254 A262605 A092731 * A161829 A290705 A115456

Adjacent sequences:  A201564 A201565 A201566 * A201568 A201569 A201570

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 03 2011

STATUS

approved

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Last modified April 18 05:44 EDT 2021. Contains 343072 sequences. (Running on oeis4.)