A129227 a(n) is that prime number, p, less than n*Pi such that n*Pi/p has the smallest fractional part.

3, 3, 3, 11, 5, 17, 7, 5, 7, 31, 17, 37, 37, 43, 47, 5, 53, 53, 59, 31, 13, 23, 71, 73, 13, 79, 83, 29, 13, 47, 97, 97, 103, 53, 109, 113, 29, 17, 61, 31, 127, 131, 67, 137, 47, 71, 73, 149, 151, 157, 157, 163, 83, 167, 43, 173, 179, 181, 37, 47, 191, 97, 197, 67, 17, 103

Offset: 1

Author

Axel Harvey, Apr 04 2007

Keywords

• easy
• nonn

Examples

			a(4)=11 because 4*Pi/11 = 1.142... and the fractional part 0.142... represents the smallest remainder resulting from the division of 4*Pi by a prime number less than 4*Pi.
		

Crossrefs

Cf. A129228.

Programs

Mathematica

f[n_] := (p = Denominator[ Min[ FractionalPart[(n*Pi / Prime@ Range@ PrimePi[n*Pi])]] [[2]]]; If[p == 1, n, p]); Array[f, 66] (* Robert G. Wilson v, Apr 08 2007 *)

Sage

A129227 = lambda n: sorted(primes(floor(n*pi)+1), key=lambda p: (n*pi/p-floor(n*pi/p)))[0] # D. S. McNeil, Dec 11 2010

Extensions

Edited and extended by Robert G. Wilson v, Apr 08 2007