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A201653 Decimal expansion of greatest x satisfying 6*x^2 = csc(x) and 0 < x < Pi. 3
3, 1, 2, 4, 5, 1, 9, 9, 1, 2, 5, 0, 1, 3, 8, 7, 6, 9, 3, 9, 6, 8, 8, 0, 1, 9, 6, 5, 0, 1, 1, 6, 2, 4, 9, 9, 4, 1, 4, 4, 8, 7, 8, 6, 3, 8, 0, 3, 1, 2, 5, 4, 7, 4, 3, 5, 3, 6, 7, 5, 6, 7, 1, 9, 1, 1, 5, 1, 2, 3, 6, 6, 8, 1, 2, 3, 6, 1, 2, 8, 1, 1, 4, 9, 6, 9, 6, 4, 8, 0, 0, 1, 1, 1, 0, 0, 4, 6, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018
CROSSREFS
Cf. A201564.
Sequence in context: A108038 A151845 A230448 * A230765 A250306 A120577
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 03 2011
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)