A201672 Decimal expansion of least x satisfying 6*x^2 - 1 = csc(x) and 0<x<Pi.

6, 6, 1, 7, 3, 6, 5, 5, 7, 1, 6, 9, 7, 4, 4, 2, 2, 6, 2, 4, 1, 8, 2, 9, 8, 3, 7, 0, 9, 4, 0, 0, 2, 6, 0, 7, 7, 4, 7, 4, 7, 9, 8, 8, 1, 3, 8, 2, 5, 3, 8, 4, 1, 0, 2, 5, 2, 2, 4, 5, 7, 7, 6, 0, 7, 8, 5, 2, 8, 6, 9, 1, 9, 6, 5, 1, 3, 1, 9, 6, 9, 6, 0, 3, 3, 1, 1, 1, 0, 9, 3, 6, 1, 5, 6, 2, 0, 0, 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:  0.66173655716974422624182983709400260774...
greatest:  3.12421996270608159489890621092028546...

Mathematica

a = 6; 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]     (* A201672 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]     (* A201673 *)

Prog

(PARI) a=6; c=-1; solve(x=.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018

Crossrefs

Cf. A201564.

Sequence in context: A112302 A073012 A102522 * A200299 A254134 A194597

Adjacent sequences: A201669 A201670 A201671 * A201673 A201674 A201675

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved