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A201676
Decimal expansion of least x satisfying 8*x^2 - 1 = csc(x) and 0<x<Pi.
3
5, 9, 1, 0, 3, 8, 4, 5, 6, 3, 4, 1, 7, 9, 2, 3, 5, 6, 7, 5, 1, 1, 9, 5, 4, 8, 1, 8, 2, 5, 4, 6, 8, 7, 4, 6, 7, 5, 9, 3, 3, 3, 7, 2, 2, 1, 8, 8, 2, 7, 7, 1, 7, 2, 8, 0, 7, 2, 3, 4, 1, 2, 8, 2, 6, 1, 1, 6, 7, 4, 3, 3, 0, 0, 3, 1, 5, 1, 9, 7, 1, 8, 0, 8, 7, 5, 5, 4, 1, 5, 4, 6, 9, 6, 5, 4, 3, 9, 9
OFFSET
0,1
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.591038456341792356751195481825468746759333...
greatest: 3.128657013857735929983404048440286781650...
MATHEMATICA
a = 8; 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, .5, .6}, WorkingPrecision -> 110]
RealDigits[r] (* A201676 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r] (* A201677 *)
PROG
(PARI) a=8; c=-1; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018
CROSSREFS
Cf. A201564.
Sequence in context: A306778 A019705 A269957 * A199797 A188616 A377559
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 04 2011
STATUS
approved