A200617 Decimal expansion of the greater of two values of x satisfying 4*x^2 - 1 = tan(x) and 0 < x < Pi/2.

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

Offset: 1

Author

Clark Kimberling, Nov 20 2011

Keywords

• nonn
• cons

Comments

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

Examples

			lesser:  0.839582259045302941513764008863804986308...
greater: 1.350956593976519397744696294368524715373...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A200614, A200616.

Programs

Mathematica

a = 4; 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, .6, .7}, WorkingPrecision -> 110]
RealDigits[r]   (* A200616 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200617 *)