

A161867


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


4



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
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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 A311012 A311013
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



