A201530 Decimal expansion of greatest x satisfying 10*x^2 - 1 = sec(x) and 0 < x < Pi.

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

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:  0.4600006985794904216969349833844460938634...
greatest: 1.52590577141056614542926620695066975318...

Mathematica

a = 10; 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, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201529 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201530 *)

Crossrefs

Cf. A201397.

Sequence in context: A339161 A142702 A236184 * A085997 A071546 A154649

Adjacent sequences: A201527 A201528 A201529 * A201531 A201532 A201533

Keyword

nonn,cons

Author

Clark Kimberling, Dec 02 2011

Status

approved