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A201581 Decimal expansion of greatest x satisfying x^2 + 10 = csc(x) and 0 < x < Pi. 3
3, 0, 9, 0, 4, 2, 1, 2, 7, 0, 1, 5, 2, 1, 5, 1, 4, 5, 3, 6, 5, 1, 4, 9, 7, 4, 4, 3, 8, 9, 9, 9, 2, 0, 5, 3, 4, 3, 8, 7, 8, 8, 2, 1, 3, 8, 3, 1, 5, 6, 3, 5, 0, 1, 4, 0, 8, 5, 5, 5, 5, 1, 8, 9, 9, 6, 6, 3, 6, 3, 1, 5, 9, 8, 0, 6, 4, 7, 6, 1, 2, 8, 4, 0, 6, 0, 6, 1, 1, 0, 6, 8, 9, 9, 4, 4, 5, 3, 4 (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:  0.100066884072919309279805384459381115060...

greatest:  3.090421270152151453651497443899920534...

MATHEMATICA

a = 1; c = 10;

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, .2}, WorkingPrecision -> 110]

RealDigits[r]   (* A201578 *)

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

RealDigits[r]   (* A201581 *)

PROG

(PARI) a=1; c=10; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

CROSSREFS

Cf. A201564.

Sequence in context: A019827 A329284 A269557 * A164597 A167295 A079442

Adjacent sequences:  A201578 A201579 A201580 * A201582 A201583 A201584

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 03 2011

STATUS

approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)