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A201665 Decimal expansion of greatest x satisfying 2*x^2 - 1 = csc(x) and 0<x<Pi. 3
3, 0, 8, 6, 1, 5, 8, 7, 7, 4, 3, 7, 7, 1, 2, 7, 1, 8, 1, 2, 2, 5, 9, 4, 8, 2, 8, 6, 3, 5, 8, 2, 1, 4, 5, 2, 4, 9, 8, 5, 3, 3, 6, 2, 2, 2, 6, 5, 7, 2, 2, 3, 1, 2, 0, 5, 5, 0, 0, 3, 9, 9, 0, 9, 2, 5, 4, 4, 4, 8, 6, 8, 6, 5, 9, 4, 8, 8, 2, 3, 8, 2, 7, 4, 4, 0, 4, 8, 0, 4, 6, 9, 4, 9, 0, 8, 0, 2, 7 (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:  1.039245650797247793231929327242483730000...

greatest:  3.086158774377127181225948286358214524...

MATHEMATICA

a = 2; 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, 1.0, 1.1}, WorkingPrecision -> 110]

RealDigits[r]     (* A201664 *)

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

RealDigits[r]      (* A201665 *)

PROG

(PARI) a=2; 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: A248424 A292525 A275975 * A137204 A021328 A178114

Adjacent sequences:  A201662 A201663 A201664 * A201666 A201667 A201668

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 04 2011

STATUS

approved

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)