A201523 Decimal expansion of least x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.

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

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:  0.557895175779035299832869736313873...
greatest: 1.5032621521314930999190799075200...

Mathematica

a = 7; 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, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201523 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201524 *)

Crossrefs

Cf. A201397.

Sequence in context: A120220 A320639 A153105 * A196348 A196351 A154583

Adjacent sequences: A201520 A201521 A201522 * A201524 A201525 A201526

Keyword

nonn,cons

Author

Clark Kimberling, Dec 02 2011

Status

approved