A201406 Decimal expansion of least x satisfying 2*x^2 = sec(x) and 0 < x < Pi.

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..98.

Example

least:  0.892874306058961124447371969018677514...
greatest: 1.2390826209275819187151092399019855...

Mathematica

a = 2; c = 0;
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, .8, 1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201406 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
RealDigits[r]   (* A201407 *)

Crossrefs

Cf. A201397.

Sequence in context: A090929 A113210 A021116 * A242972 A198142 A336056

Adjacent sequences: A201403 A201404 A201405 * A201407 A201408 A201409

Keyword

nonn,cons

Author

Clark Kimberling, Dec 01 2011

Status

approved