A201420 Decimal expansion of least x satisfying 9*x^2 = sec(x) and 0 < x < Pi.

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

Offset: 0

Author

Clark Kimberling, Dec 02 2011

Keywords

• nonn
• cons

Comments

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least:  0.3435193844487517285157937916054768...
greatest: 1.52286717667793005738690747334562...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201397.

Programs

Mathematica

a = 9; c = 0;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
RealDigits[r]     (* A201420 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201421 *)