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A201565 Decimal expansion of greatest x satisfying x^2 + 2 = csc(x) and 0 < x < Pi. 2
3, 0, 5, 3, 1, 5, 1, 7, 2, 2, 5, 2, 4, 8, 7, 0, 2, 1, 1, 8, 0, 4, 1, 5, 5, 0, 5, 3, 1, 7, 8, 1, 1, 3, 7, 4, 5, 9, 6, 2, 2, 4, 7, 6, 7, 8, 3, 9, 2, 0, 5, 5, 3, 4, 7, 5, 4, 1, 5, 4, 4, 1, 3, 9, 0, 6, 3, 7, 7, 3, 7, 1, 6, 9, 0, 6, 9, 5, 2, 2, 2, 7, 9, 1, 6, 9, 7, 4, 3, 4, 0, 3, 5, 9, 3, 5, 7, 5, 5 (list; constant; graph; refs; listen; history; text; internal format)
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:  0.46758094406347136736141927076686538859402537...

greatest:  3.05315172252487021180415505317811374596224...

MATHEMATICA

(* Program 1: A201564, A201565 *)

a = 1; c = 2;

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, .46, .47}, WorkingPrecision -> 110]

RealDigits[r]   (* A201564 *)

r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]

RealDigits[r]   (* A201565 *)

(* Program 2: implicit surface of u*x^2+v=csc(x) *)

f[{x_, u_, v_}] := u*x^2 + v - Csc[x];

t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, .1, 1}]}, {v, 0, 1}, {u, 2 + v, 10}];

ListPlot3D[Flatten[t, 1]]  (* for A201564 *)

PROG

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

CROSSREFS

Cf. A201564.

Sequence in context: A181884 A284662 A292031 * A088191 A179179 A291503

Adjacent sequences:  A201562 A201563 A201564 * A201566 A201567 A201568

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 03 2011

STATUS

approved

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Last modified December 15 20:10 EST 2018. Contains 318154 sequences. (Running on oeis4.)