A201520 Decimal expansion of greatest x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..99.

Example

least: 0.675482908113724228015178858190...
greatest: 1.4683742920332829376554687815...

Mathematica

a = 5; 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, .6, .7}, WorkingPrecision -> 110]
RealDigits[r]   (* A201519 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201520 *)

Crossrefs

Cf. A201397.

Sequence in context: A330154 A179371 A097455 * A179022 A021685 A071851

Adjacent sequences: A201517 A201518 A201519 * A201521 A201522 A201523

Keyword

nonn,cons

Author

Clark Kimberling, Dec 02 2011

Status

approved