A201662 Decimal expansion of greatest x satisfying 10*x^2 = csc(x) and 0 <x< Pi.

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

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

Index entries for transcendental numbers.

Example

least:  0.469931606000588922868653535061891306388300...
greatest:  3.131394253920689935444028622238747025122...

Mathematica

a = 10; c = 0;
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, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]    (* A201660 *)
r = x /.  FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]     (* A201662 *)

Prog

(PARI) a=10; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018

Crossrefs

Cf. A201564.

Sequence in context: A057024 A023892 A085417 * A373031 A274473 A280526

Adjacent sequences: A201659 A201660 A201661 * A201663 A201664 A201665

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved