A200623 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 2 = tan(x) and 0 < x < Pi/2.

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

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:  0.770896883914277182837264927358706321868754...
greater: 1.4547992135199955263707843007989445890126087...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A200614.

Programs

Mathematica

a = 5; c = 2;
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, .7, .8}, WorkingPrecision -> 110]
RealDigits[r]    (* A200622 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200623 *)