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A201675
Decimal expansion of greatest x satisfying 7*x^2 - 1 = csc(x) and 0<x<Pi.
3
3, 1, 2, 6, 7, 6, 3, 3, 5, 4, 8, 1, 7, 8, 4, 3, 9, 5, 8, 3, 2, 4, 7, 1, 0, 5, 4, 3, 0, 4, 1, 3, 9, 3, 5, 0, 0, 8, 6, 9, 5, 6, 0, 6, 7, 8, 0, 4, 2, 4, 0, 6, 1, 3, 9, 9, 3, 3, 0, 3, 2, 1, 0, 4, 5, 3, 3, 0, 3, 9, 5, 9, 0, 7, 3, 7, 1, 4, 3, 9, 0, 9, 5, 1, 1, 5, 5, 1, 5, 2, 7, 8, 9, 8, 4, 2, 3, 6, 0
OFFSET
1,1
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 0.62272709431369510379503993928652289013...
greatest: 3.12676335481784395832471054304139350...
MATHEMATICA
a = 7; c = -1;
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, .6, .7}, WorkingPrecision -> 110]
RealDigits[r] (* A201674 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r] (* A201675 *)
PROG
(PARI) a=7; c=-1; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018
CROSSREFS
Cf. A201564.
Sequence in context: A318552 A183289 A183253 * A279859 A201655 A049917
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 04 2011
STATUS
approved