A201664 Decimal expansion of least x satisfying 2*x^2 - 1 = csc(x) and 0<x<Pi.

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

Offset

1,3

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:  1.039245650797247793231929327242483730000...
greatest:  3.086158774377127181225948286358214524...

Mathematica

a = 2; 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, 1.0, 1.1}, WorkingPrecision -> 110]
RealDigits[r]     (* A201664 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r]      (* A201665 *)

Prog

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

Crossrefs

Cf. A201564.

Sequence in context: A114875 A275371 A225357 * A103824 A155080 A010780

Adjacent sequences: A201661 A201662 A201663 * A201665 A201666 A201667

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved