A201654 Decimal expansion of least x satisfying 7*x^2 = csc(x) and 0 < x < Pi.

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

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:  0.53109378322877556954245426287272878812709738...
greatest:  3.12698210171419101601393999273016371798979...

Mathematica

a = 7; 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]   (* A201654 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201655 *)

Prog

(PARI) a=7; 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: A181886 A126853 A286127 * A265606 A368602 A132199

Adjacent sequences: A201651 A201652 A201653 * A201655 A201656 A201657

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved