A201299 Decimal expansion of x satisfying x^2 - 5 = cot(x) and 0 < x < Pi.

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

			2.10092937702728594080037375567935559363...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201280.

Programs

Mathematica

a = 1; c = -5;
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, 2.0, 2.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201299 *)

Extensions

a(94) onwards corrected by Georg Fischer, Aug 03 2021