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A201656
Decimal expansion of least x satisfying 8*x^2 = csc(x) and 0 < x < Pi.
3
5, 0, 7, 2, 6, 2, 1, 9, 9, 3, 4, 9, 1, 0, 3, 7, 7, 8, 2, 6, 5, 8, 1, 2, 1, 4, 7, 7, 2, 6, 4, 0, 4, 1, 9, 7, 6, 3, 8, 5, 8, 6, 3, 1, 5, 1, 4, 1, 8, 5, 6, 3, 4, 8, 1, 6, 0, 9, 3, 5, 5, 8, 2, 8, 6, 9, 5, 1, 8, 0, 6, 5, 0, 1, 7, 6, 0, 7, 2, 3, 7, 3, 1, 3, 4, 4, 3, 8, 5, 7, 9, 3, 3, 9, 6, 1, 2, 3, 5
OFFSET
0,1
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.507262199349103778265812147726404197638586...
greatest: 3.128823571901654937275752484725028832935...
MATHEMATICA
a = 8; c = 0;
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] (* A201656 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r] (* A201657 *)
PROG
(PARI) a=8; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018
CROSSREFS
Cf. A201564.
Sequence in context: A199062 A328900 A070595 * A168195 A333507 A345327
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 04 2011
STATUS
approved