A201580 Decimal expansion of greatest x satisfying x^2 + 9 = csc(x) and 0 < x < Pi.

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

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:  0.111187649530336552411321691800657533611...
greatest:  3.087609602783606133001190498846701507...

Mathematica

a = 1; c = 9;
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, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201578 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201580 *)

Prog

(PARI) a=1; c=9; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

Crossrefs

Cf. A201564.

Sequence in context: A021328 A178114 A107370 * A234518 A068458 A238258

Adjacent sequences: A201577 A201578 A201579 * A201581 A201582 A201583

Keyword

nonn,cons

Author

Clark Kimberling, Dec 03 2011

Status

approved