A201656 Decimal expansion of least x satisfying 8*x^2 = csc(x) and 0 < x < Pi.

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

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:  0.507262199349103778265812147726404197638586...
greatest:  3.128823571901654937275752484725028832935...

Mathematica

a = 8; 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, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201656 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201657 *)

Prog

(PARI) a=8; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

Crossrefs

Cf. A201564.

Sequence in context: A199062 A328900 A070595 * A168195 A333507 A345327

Adjacent sequences: A201653 A201654 A201655 * A201657 A201658 A201659

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved