login
A201682
Decimal expansion of least x satisfying x^2 - 2 = csc(x) and 0<x<Pi.
3
1, 7, 3, 6, 0, 3, 2, 4, 0, 9, 7, 3, 9, 9, 9, 5, 0, 6, 5, 4, 1, 8, 3, 1, 1, 0, 7, 7, 4, 0, 4, 2, 8, 5, 2, 3, 1, 2, 7, 7, 2, 6, 5, 8, 9, 8, 1, 9, 9, 8, 4, 6, 3, 6, 6, 4, 4, 7, 4, 4, 7, 6, 3, 7, 1, 9, 2, 1, 9, 4, 3, 1, 8, 7, 3, 3, 2, 6, 5, 0, 3, 8, 5, 1, 7, 0, 1, 7, 2, 1, 4, 3, 4, 4, 6, 9, 7, 1, 5
OFFSET
1,2
COMMENTS
See A201564 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least: 1.7360324097399950654183110774042852312772...
greatest: 2.9979969201816952606618233312541258876...
MATHEMATICA
a = 1; c = -2;
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, 1.7, 1.8}, WorkingPrecision -> 110]
RealDigits[r] (* A201682 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r] (* A201683 *)
PROG
(PARI) a=1; c=-2; solve(x=1.5, 2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018
CROSSREFS
Cf. A201564.
Sequence in context: A360094 A030760 A329084 * A021580 A194557 A241002
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 04 2011
STATUS
approved