A200682 Decimal expansion of the greater of two values of x satisfying 3*x^2 = tan(x) and 0 < x < Pi/2.

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

Offset

1,2

Comments

See A200614 for a guide to related sequences. The Mathematica program includes a graph.

Links

Table of n, a(n) for n=1..99.

Example

lesser:  0.34742576447743871128905641295532587...
greater: 1.40306042080937123884892134944944201...

Mathematica

a = 3; c = 0;
f[x_] := a*x^2 - c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
RealDigits[r] (* A200681 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A200682 *)

Crossrefs

Cf. A200614.

Sequence in context: A281653 A327305 A290328 * A263618 A156788 A130801

Adjacent sequences: A200679 A200680 A200681 * A200683 A200684 A200685

Keyword

nonn,cons

Author

Clark Kimberling, Nov 20 2011

Status

approved