A201419 Decimal expansion of greatest x satisfying 8*x^2 = sec(x) and 0 < x < Pi.

1, 5, 1, 6, 4, 0, 9, 8, 4, 8, 1, 1, 1, 9, 3, 5, 5, 8, 9, 6, 3, 6, 2, 1, 8, 9, 4, 0, 7, 7, 5, 1, 9, 7, 0, 8, 0, 7, 6, 6, 7, 9, 5, 6, 1, 1, 8, 2, 4, 4, 3, 0, 6, 3, 4, 7, 6, 0, 8, 6, 1, 0, 3, 9, 9, 9, 5, 2, 4, 0, 4, 5, 1, 7, 0, 0, 0, 1, 2, 8, 9, 8, 1, 1, 2, 1, 9, 0, 3, 9, 7, 8, 2, 8, 9, 3, 9, 6, 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:  0.365868442181046909444887950918036646081...
greatest: 1.5164098481119355896362189407751970807...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201397.

Programs

Mathematica

a = 8; 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]    (* A201418 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201419 *)