A201675 Decimal expansion of greatest x satisfying 7*x^2 - 1 = csc(x) and 0<x<Pi.

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

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

Index entries for transcendental numbers.

Example

least:  0.62272709431369510379503993928652289013...
greatest:  3.12676335481784395832471054304139350...

Mathematica

a = 7; c = -1;
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, .6, .7}, WorkingPrecision -> 110]
RealDigits[r]     (* A201674 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r]     (* A201675 *)

Prog

(PARI) a=7; c=-1; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018

Crossrefs

Cf. A201564.

Sequence in context: A318552 A183289 A183253 * A279859 A201655 A049917

Adjacent sequences: A201672 A201673 A201674 * A201676 A201677 A201678

Keyword

nonn,cons

Author

Clark Kimberling, Dec 04 2011

Status

approved