A201666 Decimal expansion of least x satisfying 3*x^2 - 1 = csc(x) and 0

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

Offset: 0

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:  0.875943738724356441549462867955303876323370...
greatest:  3.105791229363082277928967931614314303595...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A201564.

Programs

Mathematica

a = 3; 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, .8, .9}, WorkingPrecision -> 110]
RealDigits[r]     (* A201666 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r]     (* A201667 *)

PARI

a=3; c=-1; solve(x=.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018