A135296 A measure of quality (the higher the better) for the approximation to Pi by rationals A022853(n)/n.

7, 3, 2, 2, 3, 6, 112, 7, 3, 2, 2, 3, 6, 56, 8, 3, 2, 2, 3, 5, 37, 8, 3, 2, 2, 3, 5, 28, 9, 4, 2, 2, 3, 5, 22, 10, 4, 2, 2, 2, 5, 18, 11, 4, 2, 2, 2, 4, 16, 12, 4, 2, 2, 2, 4, 14, 14, 4, 2, 2, 2, 4, 12, 16, 4, 2, 2, 2, 4, 11, 18, 5, 2, 2, 2, 4, 10, 22, 5, 3, 2, 2, 4, 9, 28, 5, 3, 2, 2

Offset: 1

Author

Franz Vrabec, Dec 04 2007

Keywords

• nonn
• look

Examples

			a(7)=112 because [1/|7*Pi-22|] = [1/|-0.0088514|] = [112.976] = 112.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A022853.

Programs

Mathematica

a = {}; For[n = 1, n < 90, n++, AppendTo[a, Floor[1/(If[FractionalPart[n*Pi] > 1/2, Ceiling[n*Pi] - n*Pi, n*Pi - Floor[n*Pi]])]]]; a (* Stefan Steinerberger, Dec 05 2007 *)

Formula

a(n) = [1/|n*Pi-A022853(n)|].

Extensions

More terms from Stefan Steinerberger, Dec 05 2007