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A201591
Decimal expansion of least x satisfying 6*x^2 = csc(x) and 0 < x < Pi.
3
5, 6, 0, 1, 0, 0, 6, 9, 4, 9, 1, 2, 1, 6, 0, 7, 6, 2, 8, 2, 3, 8, 4, 1, 3, 3, 3, 7, 9, 7, 8, 1, 2, 0, 7, 7, 5, 2, 9, 3, 7, 4, 5, 0, 3, 0, 3, 0, 8, 9, 6, 4, 1, 1, 5, 5, 8, 6, 1, 2, 2, 0, 4, 3, 0, 9, 0, 6, 7, 5, 9, 1, 6, 2, 1, 5, 6, 4, 8, 3, 3, 1, 4, 0, 8, 0, 7, 1, 6, 1, 7, 3, 2, 2, 0, 2, 3, 8, 9, 3, 3
OFFSET
0,1
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.56010069491216076282384133379781207752937450...
greatest: 3.12451991250138769396880196501162499414487...
MATHEMATICA
a = 6; 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] (* A201591 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r] (* A201653 *)
PROG
(PARI) a=6; 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: A215833 A110800 A021645 * A100220 A011440 A375957
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 03 2011
EXTENSIONS
Terms a(90) onward corrected by G. C. Greubel, Aug 22 2018
STATUS
approved