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A201566
Decimal expansion of least x satisfying x^2 + 3 = csc(x) and 0 < x < Pi.
2
3, 2, 7, 6, 4, 8, 2, 4, 7, 1, 1, 3, 6, 6, 8, 6, 7, 8, 0, 9, 8, 2, 4, 7, 7, 0, 6, 2, 0, 9, 8, 1, 9, 5, 2, 9, 8, 4, 4, 3, 7, 8, 4, 5, 2, 8, 2, 0, 0, 2, 4, 4, 8, 6, 4, 8, 9, 9, 2, 1, 7, 0, 7, 4, 8, 2, 1, 6, 1, 7, 1, 2, 6, 7, 5, 1, 4, 2, 8, 3, 5, 6, 9, 6, 9, 5, 8, 9, 9, 8, 1, 6, 1, 6, 1, 7, 2, 1, 8
OFFSET
0,1
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.3276482471136686780982477062098195298...
greatest: 3.0606476216743906494670210614415753...
MATHEMATICA
a = 1; c = 3;
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, .3, .4}, WorkingPrecision -> 110]
RealDigits[r] (* A201567 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r] (* A201568 *)
PROG
(PARI) a=1; c=3; solve(x=0.2, 0.5, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018
CROSSREFS
Cf. A201564.
Sequence in context: A269402 A268934 A268832 * A072764 A364832 A349890
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 03 2011
STATUS
approved