A201676 Decimal expansion of least x satisfying 8*x^2 - 1 = csc(x) and 0<x<Pi.

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

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:  0.591038456341792356751195481825468746759333...
greatest:  3.128657013857735929983404048440286781650...

Mathematica

a = 8; 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, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]     (* A201676 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r]     (* A201677 *)

Prog

(PARI) a=8; c=-1; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018

Crossrefs

Cf. A201564.

Sequence in context: A306778 A019705 A269957 * A199797 A188616 A377559

Adjacent sequences: A201673 A201674 A201675 * A201677 A201678 A201679

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved