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A201738 Decimal expansion of greatest x satisfying x^2 - 4 = csc(x) and 0<x<Pi. 3
2, 9, 1, 8, 3, 4, 3, 6, 9, 9, 0, 1, 8, 2, 0, 1, 3, 8, 7, 6, 5, 9, 8, 3, 6, 9, 9, 2, 0, 7, 6, 0, 5, 8, 7, 6, 7, 2, 1, 0, 5, 9, 1, 6, 3, 5, 4, 8, 7, 2, 2, 2, 8, 8, 1, 3, 4, 7, 2, 0, 4, 0, 6, 7, 8, 4, 2, 0, 1, 0, 6, 9, 8, 9, 3, 9, 1, 9, 7, 2, 7, 1, 2, 6, 0, 3, 0, 2, 6, 3, 1, 7, 2 (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.
There is a greatest number c for which x^2-c=csc(x) for some number x satisfying 0<x<pi. The number c is between 4 and 5.
LINKS
EXAMPLE
least: 2.31504693361737481767157626271919435080...
greatest: 2.91834369901820138765983699207605876...
MATHEMATICA
a = 1; c = -4;
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, 2.3, 2.4}, WorkingPrecision -> 110]
RealDigits[r] (* A201737 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r] (* A201738 *)
PROG
(PARI) a=1; c=-4; solve(x=2.5, 3, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018
CROSSREFS
Cf. A201564.
Sequence in context: A096250 A016595 A144806 * A201749 A117033 A152584
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 04 2011
STATUS
approved

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Last modified March 29 08:53 EDT 2024. Contains 371268 sequences. (Running on oeis4.)