A201518 Decimal expansion of greatest x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.

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

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:  0.774427257079893623257029009000...
greatest: 1.4313635500690391357640449937...

Mathematica

a = 4; 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, .7, .8}, WorkingPrecision -> 110]
RealDigits[r]   (* A201517 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A201518 *)

Crossrefs

Cf. A201397.

Sequence in context: A197700 A006467 A119505 * A168616 A342813 A296218

Adjacent sequences: A201515 A201516 A201517 * A201519 A201520 A201521

Keyword

nonn,cons

Author

Clark Kimberling, Dec 02 2011

Status

approved