A201661 Decimal expansion of least x satisfying x^2 - 1 = csc(x) and 0

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

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:  1.4183556185449426563353062368720819193360860...
greatest:  3.0179424745361512278525720832771672528942...
		

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 = -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, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]     (* A201661 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r]     (* A201663 *)

PARI

a=1; c=-1; solve(x=1, 2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018