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A201569 Decimal expansion of greatest x satisfying x^2 + 4 = csc(x) and 0 < x < Pi. 3
3, 0, 6, 6, 9, 3, 0, 1, 7, 7, 6, 5, 5, 7, 9, 6, 7, 1, 5, 9, 2, 1, 0, 6, 2, 7, 1, 3, 7, 3, 8, 1, 9, 8, 0, 7, 6, 4, 5, 0, 3, 0, 6, 2, 1, 6, 7, 1, 9, 0, 4, 5, 6, 7, 5, 9, 0, 8, 5, 3, 0, 1, 7, 8, 9, 3, 4, 9, 7, 7, 9, 4, 1, 5, 5, 5, 0, 6, 8, 7, 0, 1, 3, 2, 5, 0, 4, 0, 0, 1, 4, 8, 0, 6, 4, 8, 0, 3, 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:  0.2487490007162959853652924083716941039...

greatest:  3.0669301776557967159210627137381980...

MATHEMATICA

a = 1; c = 4;

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, .3}, WorkingPrecision -> 110]

RealDigits[r]   (* A201568 *)

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

RealDigits[r]   (* A201569 *)

PROG

(PARI) a=1; c=4; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

CROSSREFS

Cf. A201564.

Sequence in context: A004606 A019808 A182145 * A056459 A021330 A199055

Adjacent sequences:  A201566 A201567 A201568 * A201570 A201571 A201572

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 03 2011

STATUS

approved

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Last modified January 15 18:52 EST 2019. Contains 319170 sequences. (Running on oeis4.)