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A201653 Decimal expansion of greatest x satisfying 6*x^2 = csc(x) and 0 < x < Pi. 3
3, 1, 2, 4, 5, 1, 9, 9, 1, 2, 5, 0, 1, 3, 8, 7, 6, 9, 3, 9, 6, 8, 8, 0, 1, 9, 6, 5, 0, 1, 1, 6, 2, 4, 9, 9, 4, 1, 4, 4, 8, 7, 8, 6, 3, 8, 0, 3, 1, 2, 5, 4, 7, 4, 3, 5, 3, 6, 7, 5, 6, 7, 1, 9, 1, 1, 5, 1, 2, 3, 6, 6, 8, 1, 2, 3, 6, 1, 2, 8, 1, 1, 4, 9, 6, 9, 6, 4, 8, 0, 0, 1, 1, 1, 0, 0, 4, 6, 9 (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:  0.56010069491216076282384133379781207752937450...

greatest:  3.12451991250138769396880196501162499414487...

MATHEMATICA

a = 6; 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, .5, .6}, WorkingPrecision -> 110]

RealDigits[r]   (* A201591 *)

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

RealDigits[r]   (* A201653 *)

PROG

(PARI) a=6; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

CROSSREFS

Cf. A201564.

Sequence in context: A108038 A151845 A230448 * A230765 A250306 A120577

Adjacent sequences:  A201650 A201651 A201652 * A201654 A201655 A201656

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 03 2011

STATUS

approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)