A200615 Decimal expansion of the greater of two values of x satisfying 3*x^2 - 1 = tan(x) and 0 < x < Pi/2.

1, 3, 5, 0, 9, 5, 6, 5, 9, 3, 9, 7, 6, 5, 1, 9, 3, 9, 7, 7, 4, 4, 6, 9, 6, 2, 9, 4, 3, 6, 8, 5, 2, 4, 7, 1, 5, 3, 7, 3, 0, 3, 7, 3, 0, 1, 6, 7, 5, 8, 8, 2, 5, 6, 2, 9, 7, 8, 8, 4, 4, 6, 2, 0, 4, 7, 6, 6, 0, 1, 7, 1, 8, 4, 6, 3, 4, 3, 8, 0, 2, 8, 2, 8, 5, 3, 9, 6, 5, 0, 6, 3, 4, 5, 9, 4, 4, 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:  0.839582259045302941513764008863804986308...
greater: 1.350956593976519397744696294368524715373...

Mathematica

a = 3; c = 1;
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, .8, .9}, WorkingPrecision -> 110]
RealDigits[r]   (* A200614 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200615 *)

Crossrefs

Cf. A200338.

Sequence in context: A248192 A323987 A124222 * A349605 A318204 A306637

Adjacent sequences: A200612 A200613 A200614 * A200616 A200617 A200618

Keyword

nonn,cons

Author

Clark Kimberling, Nov 20 2011

Status

approved