A201526 Decimal expansion of greatest x satisfying 8*x^2 - 1 = sec(x) and 0 < x < Pi.

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

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:  0.518577002201711458253109820417244...
greatest: 1.5130057374477490977746930540120...

Mathematica

a = 8; 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]   (* A201525 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201526 *)

Crossrefs

Cf. A201397.

Sequence in context: A318068 A165449 A019114 * A091384 A011305 A348317

Adjacent sequences: A201523 A201524 A201525 * A201527 A201528 A201529

Keyword

nonn,cons

Author

Clark Kimberling, Dec 02 2011

Status

approved