A201519 Decimal expansion of least x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

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

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:  0.675482908113724228015178858190...
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: A100124 A355336 A190648 * A198507 A021152 A199720

Adjacent sequences: A201516 A201517 A201518 * A201520 A201521 A201522

Keyword

nonn,cons

Author

Clark Kimberling, Dec 02 2011

Status

approved