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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
OFFSET
1,1
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
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
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 04 2011
STATUS
approved