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A201576
Decimal expansion of least x satisfying x^2 + 8 = csc(x) and 0 < x < Pi.
3
1, 2, 5, 0, 8, 1, 9, 2, 2, 6, 3, 5, 9, 9, 7, 4, 4, 1, 2, 8, 9, 1, 7, 7, 7, 0, 1, 6, 5, 3, 7, 8, 5, 7, 0, 7, 1, 8, 7, 6, 5, 5, 4, 8, 7, 1, 3, 4, 6, 8, 7, 6, 2, 6, 4, 8, 0, 7, 0, 8, 7, 1, 4, 2, 1, 6, 3, 6, 8, 2, 8, 2, 2, 8, 9, 2, 4, 8, 7, 3, 4, 6, 3, 7, 1, 4, 1, 7, 7, 6, 1, 6, 6, 7, 2, 8, 5, 5, 2
OFFSET
0,2
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.125081922635997441289177701653785707187...
greatest: 3.084464140564380849459190595364646021...
MATHEMATICA
a = 1; c = 8;
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, .2}, WorkingPrecision -> 110]
RealDigits[r] (* A201576 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r] (* A201577 *)
PROG
(PARI) a=1; c=8; solve(x=0.1, 0.2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018
CROSSREFS
Cf. A201564.
Sequence in context: A331165 A022832 A008348 * A265299 A020836 A349353
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 03 2011
STATUS
approved