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A201672
Decimal expansion of least x satisfying 6*x^2 - 1 = csc(x) and 0<x<Pi.
3
6, 6, 1, 7, 3, 6, 5, 5, 7, 1, 6, 9, 7, 4, 4, 2, 2, 6, 2, 4, 1, 8, 2, 9, 8, 3, 7, 0, 9, 4, 0, 0, 2, 6, 0, 7, 7, 4, 7, 4, 7, 9, 8, 8, 1, 3, 8, 2, 5, 3, 8, 4, 1, 0, 2, 5, 2, 2, 4, 5, 7, 7, 6, 0, 7, 8, 5, 2, 8, 6, 9, 1, 9, 6, 5, 1, 3, 1, 9, 6, 9, 6, 0, 3, 3, 1, 1, 1, 0, 9, 3, 6, 1, 5, 6, 2, 0, 0, 2
OFFSET
0,1
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.66173655716974422624182983709400260774...
greatest: 3.12421996270608159489890621092028546...
MATHEMATICA
a = 6; 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, .6, .7}, WorkingPrecision -> 110]
RealDigits[r] (* A201672 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r] (* A201673 *)
PROG
(PARI) a=6; c=-1; solve(x=.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018
CROSSREFS
Cf. A201564.
Sequence in context: A112302 A073012 A102522 * A200299 A254134 A194597
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 04 2011
STATUS
approved