A201583 Decimal expansion of least x satisfying 2*x^2 = csc(x) and 0<x<Pi.

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

Offset

0,1

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 = 0..10000

Example

least:  0.825028924015006339333946318183357978692...
greatest:  3.089174211929930206560577487869973804...

Mathematica

a = 2; 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, .8, .9}, WorkingPrecision -> 110]
RealDigits[r]    (* A201583 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]    (* A201584 *)

Prog

(PARI) a=2; 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: A109614 A248301 A284157 * A243370 A179048 A173158

Adjacent sequences: A201580 A201581 A201582 * A201584 A201585 A201586

Keyword

nonn,cons

Author

Clark Kimberling, Dec 03 2011

Status

approved