A200633 Decimal expansion of the lesser of two values of x satisfying 6*x^2 - 1 = tan(x) and 0 < x < Pi/2.

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..98.

Example

lesser:  0.50974170891854848924604966585258686270831...
greater: 1.48978365608349822096681798686067147504261...

Mathematica

a = 6; 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, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A200633 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200634 *)

Crossrefs

Cf. A200614.

Sequence in context: A196769 A019925 A101115 * A196820 A176325 A275792

Adjacent sequences: A200630 A200631 A200632 * A200634 A200635 A200636

Keyword

nonn,cons

Author

Clark Kimberling, Nov 20 2011

Status

approved