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A201671 Decimal expansion of greatest x satisfying 5*x^2 - 1 = csc(x) and 0<x<Pi. 3
3, 1, 2, 0, 6, 2, 2, 9, 9, 3, 0, 8, 6, 9, 1, 8, 8, 0, 5, 1, 4, 1, 2, 7, 3, 4, 2, 4, 6, 2, 3, 0, 6, 6, 0, 0, 2, 1, 7, 0, 0, 3, 5, 6, 2, 4, 5, 2, 7, 7, 9, 7, 3, 7, 1, 1, 0, 9, 8, 7, 8, 5, 9, 1, 2, 2, 8, 1, 0, 3, 9, 7, 7, 4, 6, 4, 5, 3, 7, 4, 0, 0, 1, 4, 8, 8, 0, 6, 3, 0, 8, 4, 4, 1, 1, 7, 5, 1, 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:  0.711533888367151499246796307428212556772...

greatest:  3.120622993086918805141273424623066002...

MATHEMATICA

a = 5; 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, .7, .8}, WorkingPrecision -> 110]

RealDigits[r]     (* A201670 *)

r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]

RealDigits[r]     (* A201671 *)

PROG

(PARI) a=5; 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: A222212 A318526 A054869 * A226590 A261349 A227962

Adjacent sequences:  A201668 A201669 A201670 * A201672 A201673 A201674

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 04 2011

STATUS

approved

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Last modified December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)