A161867 Denominators of ratio of nonprimes in a square interval to that of nonprimes in that interval and its successor.

4, 8, 11, 5, 2, 7, 25, 29, 2, 35, 39, 21, 47, 2, 51, 28, 61, 64, 67, 35, 37, 79, 81, 83, 89, 93, 95, 33, 104, 2, 109, 113, 39, 121, 125, 65, 131, 133, 137, 47, 37, 151, 51, 2, 161, 165, 2, 171, 179, 89, 177, 184, 191, 49, 201, 199, 101, 207, 208, 43, 109, 55, 227, 2, 233, 119

Offset: 1

Author

Daniel Tisdale, Jun 20 2009

Keywords

• nonn
• frac

Examples

			First few ratios are 1/4, 3/8, 5/11, 2/5, 1/2, 3/7, 12/25, 13/29.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A161865, numerators for this sequence.

Programs

Mathematica

Denominator[Table[((2 n + 1) - (PrimePi[(n + 1)^2] - PrimePi[n^2]))/((4 n + 4) - (PrimePi[(n + 2)^2] - PrimePi[n^2])), {n, 1, 100}]] (* corrected by G. C. Greubel, Dec 20 2016 *)

Formula

The limit of this sequence of ratios is 1/2, as can be shown by setting an increasing lower bound on the ratio of composites in successive square intervals.

Extensions

Keyword:frac added by R. J. Mathar, Jun 30 2009

Extended beyond a(9) by R. J. Mathar, Sep 27 2009