A201516 Decimal expansion of greatest x satisfying 3*x^2 - 1 = sec(x) and 0 < x < Pi.

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

Offset: 1

Author

Clark Kimberling, Dec 02 2011

Keywords

• nonn
• cons

Comments

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least:  0.95353909754991468966727069537237822743...
greatest: 1.341430166291259764576080506763614171...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201397.

Programs

Mathematica

a = 3; c = -1;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .9, 1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201515 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A201516 *)