A200624 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 3 = tan(x) and 0 < x < Pi/2.

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

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.

Index entries for transcendental numbers.

Example

lesser:  0.9325170518642294819498571898931399897649173...
greater: 1.43443679853106488271886435135433585034396681...

Mathematica

a = 5; c = 3;
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, .93, .94}, WorkingPrecision -> 110]
RealDigits[r]    (* A200624 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200625 *)

Crossrefs

Cf. A200614.

Sequence in context: A210644 A072559 A019941 * A105171 A369880 A010538

Adjacent sequences: A200621 A200622 A200623 * A200625 A200626 A200627

Keyword

nonn,cons

Author

Clark Kimberling, Nov 20 2011

Status

approved