A201524 Decimal expansion of greatest x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.

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

Offset: 1

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:  0.557895175779035299832869736313873...
greatest: 1.5032621521314930999190799075200...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201397.

Programs

Mathematica

a = 7; c = -1;
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, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201523 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201524 *)