A201585 Decimal expansion of least x satisfying 3*x^2 = csc(x) and 0<x<Pi.

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

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:  0.71361154106545351696712348748482823114400555...
greatest:  3.10705708466927913942133639758902326551860...

Mathematica

a = 3; 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, .7, .8}, WorkingPrecision -> 110]
RealDigits[r]    (* A201585 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]    (* A201586 *)

Prog

(PARI) a=3; 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: A039616 A344967 A362923 * A089562 A104621 A331900

Adjacent sequences: A201582 A201583 A201584 * A201586 A201587 A201588

Keyword

nonn,cons

Author

Clark Kimberling, Dec 03 2011

Status

approved