A201409 Decimal expansion of greatest x satisfying 3*x^2 = sec(x) and 0 < x < Pi.

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

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:  0.6461374540628972972901679159101125226952859...
greatest: 1.39986411944606406722963950518361037394178...

Mathematica

a = 3; c = 0;
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]    (* A201408 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]    (* A201409 *)

Crossrefs

Cf. A201397.

Sequence in context: A306963 A084762 A188444 * A111120 A100401 A004166

Adjacent sequences: A201406 A201407 A201408 * A201410 A201411 A201412

Keyword

nonn,cons

Author

Clark Kimberling, Dec 01 2011

Status

approved