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A201683 Decimal expansion of greatest x satisfying x^2 - 2 = csc(x) and 0<x<Pi. 3
2, 9, 9, 7, 9, 9, 6, 9, 2, 0, 1, 8, 1, 6, 9, 5, 2, 6, 0, 6, 6, 1, 8, 2, 3, 3, 3, 1, 2, 5, 4, 1, 2, 5, 8, 8, 7, 6, 5, 4, 9, 8, 3, 3, 6, 8, 1, 2, 0, 0, 3, 2, 4, 7, 4, 8, 8, 3, 6, 5, 9, 5, 1, 9, 3, 1, 0, 9, 4, 8, 3, 3, 2, 2, 1, 8, 8, 5, 2, 1, 7, 8, 8, 0, 8, 7, 8, 1, 3, 6, 3, 4, 0, 8, 0, 2, 2, 7, 8 (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:  1.7360324097399950654183110774042852312772...

greatest:  2.9979969201816952606618233312541258876...

MATHEMATICA

a = 1; c = -2;

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, 1.7, 1.8}, WorkingPrecision -> 110]

RealDigits[r]     (* A201682 *)

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

RealDigits[r]     (* A201683 *)

PROG

(PARI) a=1; c=-2; solve(x=2.5, 3, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018

CROSSREFS

Cf. A201564.

Sequence in context: A087042 A266274 A003678 * A197394 A198942 A168333

Adjacent sequences:  A201680 A201681 A201682 * A201684 A201685 A201686

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 04 2011

STATUS

approved

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Last modified September 15 14:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)