A201418 Decimal expansion of least x satisfying 8*x^2 = sec(x) and 0 < x < Pi.

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

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:  0.365868442181046909444887950918036646081...
greatest: 1.5164098481119355896362189407751970807...

Mathematica

a = 8; 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, .3, .4}, WorkingPrecision -> 110]
RealDigits[r]     (* A201418 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201419 *)

Crossrefs

Cf. A201397.

Sequence in context: A272976 A113533 A330525 * A123688 A082284 A241474

Adjacent sequences: A201415 A201416 A201417 * A201419 A201420 A201421

Keyword

nonn,cons

Author

Clark Kimberling, Dec 01 2011

Status

approved