A201315 Decimal expansion of x satisfying x^2 - 6 = cot(x) and 0 < x < Pi.

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

Offset: 1

Author

Clark Kimberling, Nov 29 2011

Keywords

• nonn
• cons

Comments

See A201280 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			2.2709875864949953570582339829209171574530...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201280.

Programs

Mathematica

a = 1; c = -6;
f[x_] := a*x^2 + c; g[x_] := Cot[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]
RealDigits[r]   (* A201315 *)

Extensions

a(85) onwards corrected by Georg Fischer, Aug 03 2021