A200626 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 4 = tan(x) and 0 < x < Pi/2.

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

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:  1.0862483073723514930516537470257901302111...
greater: 1.4001025553369417418319593715715854730538...

Mathematica

a = 5; c = 4;
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, .9, 1.0}, WorkingPrecision -> 110]
RealDigits[r]   (* A200626 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200627 *)

Crossrefs

Cf. A200614.

Sequence in context: A365254 A021847 A029684 * A360166 A197732 A224237

Adjacent sequences: A200623 A200624 A200625 * A200627 A200628 A200629

Keyword

nonn,cons

Author

Clark Kimberling, Nov 20 2011

Status

approved