A201582 Decimal expansion of greatest x satisfying x^2 = csc(x) and 0<x<Pi.

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

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:  1.068223544197249018283471114263092898468...
greatest:  3.032645418388756188675325636802608932...

Mathematica

a = 1; 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, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A196617 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201582 *)

Prog

(PARI) a=1; c=0; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

Crossrefs

Cf. A201564, A196617.

Sequence in context: A297168 A112470 A331924 * A369881 A115379 A127801

Adjacent sequences: A201579 A201580 A201581 * A201583 A201584 A201585

Keyword

nonn,cons

Author

Clark Kimberling, Dec 03 2011

Status

approved