A201735 Decimal expansion of least x satisfying x^2 - 3 = csc(x) and 0

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

Offset: 1

Author

Clark Kimberling, Dec 04 2011

Keywords

• nonn
• cons

Comments

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least:  2.028479610685815736595839405840741960330...
greatest:  2.968711981161412446755404392723943506...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A201564.

Programs

Mathematica

a = 1; c = -3;
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, 2.0, 2.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201735 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]   (* A201736 *)

PARI

a=1; c=-3; solve(x=2, 2.5, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018