A066927 Least k such that between p and 2p, for all primes > 3, there is always a number that is twice a square, i.e.; a k such that p < 2k^2 < 2p.

2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15

Offset: 1

Author

Robert G. Wilson v, Jan 24 2002

Keywords

• easy
• nonn

Examples

			a(5) = 3. The 5th prime is 11 and 2p is 22. The theorem says that there exists a number k, between p & 2p that is twice a square. 18 is between 11 & 22 and is of the form 2k^2, k being 3.
		

Crossrefs

Cf. A006255.

Programs

Mathematica

Table[ Ceiling[ Sqrt[ Prime[ n ]/2 ] ], {n, 1, 100} ]