A201567 Decimal expansion of greatest x satisfying x^2 + 3 = csc(x) and 0 < x < Pi.

3, 0, 6, 0, 6, 4, 7, 6, 2, 1, 6, 7, 4, 3, 9, 0, 6, 4, 9, 4, 6, 7, 0, 2, 1, 0, 6, 1, 4, 4, 1, 5, 7, 5, 3, 7, 2, 7, 8, 8, 8, 9, 0, 1, 2, 3, 3, 7, 6, 9, 2, 2, 2, 7, 4, 3, 9, 7, 9, 9, 5, 2, 3, 0, 0, 1, 8, 8, 1, 8, 3, 7, 3, 7, 3, 6, 9, 0, 6, 0, 9, 4, 1, 8, 6, 6, 2, 9, 2, 4, 4, 0, 1, 7, 3, 8, 0, 7, 6

Offset

1,1

Comments

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

least:  0.3276482471136686780982477062098195298...
greatest:  3.0606476216743906494670210614415753...

Mathematica

a = 1; c = 3;
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, .3, .4}, WorkingPrecision -> 110]
RealDigits[r]    (* A201567 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201568 *)

Prog

(PARI) a=1; c=3; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

Crossrefs

Cf. A201564.

Sequence in context: A262605 A092731 A348080 * A161829 A290705 A115456

Adjacent sequences: A201564 A201565 A201566 * A201568 A201569 A201570

Keyword

nonn,cons

Author

Clark Kimberling, Dec 03 2011

Status

approved