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

1,1

Links

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

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.

Example

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

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)

Crossrefs

Cf. A161865, numerators for this sequence.

Sequence in context: A133270 A131517 A076689 * A311011 A331052 A311012

Adjacent sequences: A161864 A161865 A161866 * A161868 A161869 A161870

Keyword

nonn,frac

Author

Daniel Tisdale, Jun 20 2009

Extensions

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

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

Status

approved