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A201570
Decimal expansion of least x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.
3
1, 9, 9, 7, 4, 2, 2, 9, 2, 8, 1, 9, 4, 7, 2, 1, 3, 7, 0, 8, 6, 7, 4, 0, 5, 1, 5, 9, 5, 5, 3, 4, 8, 1, 1, 4, 5, 3, 2, 5, 4, 5, 4, 4, 3, 9, 0, 3, 2, 5, 3, 2, 4, 3, 3, 4, 5, 3, 8, 3, 3, 5, 7, 7, 9, 2, 2, 9, 6, 3, 1, 0, 3, 9, 3, 7, 2, 6, 7, 6, 1, 4, 9, 0, 4, 3, 4, 8, 2, 7, 7, 7, 7, 7, 5, 6, 0, 7, 1
OFFSET
0,2
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.19974229281947213708674051595534811453...
greatest: 3.07227983005125033585986646046469906...
MATHEMATICA
a = 1; c = 5;
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] (* A201570 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r] (* A201571 *)
PROG
(PARI) a=1; c=5; 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: A270712 A277587 A372828 * A019895 A196399 A239528
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 03 2011
STATUS
approved