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A201587 Decimal expansion of least x satisfying 4*x^2 = csc(x) and 0 < x < Pi. 3
6, 4, 4, 8, 9, 7, 4, 7, 5, 5, 4, 3, 6, 7, 3, 8, 3, 4, 4, 4, 3, 3, 5, 7, 3, 9, 0, 0, 4, 4, 4, 7, 4, 5, 2, 0, 1, 7, 0, 1, 3, 6, 8, 0, 5, 7, 9, 8, 7, 6, 3, 3, 7, 5, 0, 8, 8, 3, 4, 1, 4, 4, 8, 8, 6, 5, 5, 0, 7, 5, 9, 7, 3, 0, 8, 2, 2, 8, 5, 9, 1, 9, 6, 9, 6, 3, 7, 0, 0, 3, 0, 4, 9, 4, 5, 1, 7, 5, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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 = 0..10000

EXAMPLE

least:  0.6448974755436738344433573900444745201701368...

greatest:  3.1158390512762535211310850151952082587811...

MATHEMATICA

a = 4; c = 0;

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, .6, .7}, WorkingPrecision -> 110]

RealDigits[r]   (* A201587 *)

r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]

RealDigits[r]   (* A201588 *)

PROG

(PARI) a=4; c=0; solve(x=0.6, 0.7, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

CROSSREFS

Cf. A201564.

Sequence in context: A211268 A021612 A329281 * A110756 A200698 A013661

Adjacent sequences:  A201584 A201585 A201586 * A201588 A201589 A201590

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 03 2011

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)