A200635 Decimal expansion of the lesser of two values of x satisfying 6*x^2 - 5 = tan(x) and 0 < x < Pi/2.

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

Offset

1,3

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:  1.0650216206187079002949359361195227330132...
greater: 1.4359727977477278397377595713631806347524...

Mathematica

a = 6; c = 5;
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, 1, 1.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A200635 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200636 *)

Crossrefs

Cf. A200614.

Sequence in context: A245973 A214128 A166509 * A197261 A010773 A099288

Adjacent sequences: A200632 A200633 A200634 * A200636 A200637 A200638

Keyword

nonn,cons

Author

Clark Kimberling, Nov 20 2011

Status

approved