A201683 Decimal expansion of greatest x satisfying x^2 - 2 = csc(x) and 0<x<Pi.

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

Offset

1,1

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 = 1..10000

Example

least:  1.7360324097399950654183110774042852312772...
greatest:  2.9979969201816952606618233312541258876...

Mathematica

a = 1; c = -2;
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, 1.7, 1.8}, WorkingPrecision -> 110]
RealDigits[r]     (* A201682 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]     (* A201683 *)

Prog

(PARI) a=1; c=-2; solve(x=2.5, 3, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018

Crossrefs

Cf. A201564.

Sequence in context: A087042 A266274 A003678 * A331369 A197394 A198942

Adjacent sequences: A201680 A201681 A201682 * A201684 A201685 A201686

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved