A200621 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 1 = tan(x) and 0 < x < Pi/2.

1, 4, 6, 9, 0, 0, 2, 7, 1, 9, 5, 1, 3, 6, 1, 0, 6, 1, 3, 2, 2, 3, 3, 6, 2, 5, 9, 7, 5, 8, 3, 6, 3, 2, 4, 1, 1, 2, 7, 8, 0, 0, 0, 3, 4, 6, 1, 5, 3, 5, 7, 4, 6, 4, 8, 5, 8, 8, 7, 7, 3, 5, 8, 6, 2, 2, 8, 1, 7, 2, 0, 1, 8, 4, 8, 3, 0, 6, 1, 0, 4, 5, 6, 4, 2, 4, 9, 0, 1, 9, 0, 6, 6, 9, 7, 6, 7, 0, 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:  0.5738256142207075194706993073950289720400...
greater: 1.469002719513610613223362597583632411278000...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A200614.

Programs

Mathematica

a = 5; 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]   (* A200620 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200621 *)