A201682 Decimal expansion of least x satisfying x^2 - 2 = csc(x) and 0<x<Pi.

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

Offset

1,2

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=1.5, 2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018

Crossrefs

Cf. A201564.

Sequence in context: A360094 A030760 A329084 * A021580 A194557 A241002

Adjacent sequences: A201679 A201680 A201681 * A201683 A201684 A201685

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved