A201415 Decimal expansion of greatest x satisfying 6*x^2 = sec(x) and 0 < x < Pi.

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

Offset: 1

Author

Clark Kimberling, Dec 01 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least:  0.42800895010041097002739347769069180659...
greatest: 1.496285048607652953479229041712424469...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201397.

Programs

Mathematica

a = 6; 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, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]    (* A201414 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]    (* A201415 *)

PARI

solve(x=1,2, 6*x^2*cos(x)-1) \\ Charles R Greathouse IV, Nov 26 2024