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Denominators of ratio of nonprimes in a square interval to that of nonprimes in that interval and its successor.
4

%I #11 Dec 22 2016 22:06:25

%S 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,

%T 93,95,33,104,2,109,113,39,121,125,65,131,133,137,47,37,151,51,2,161,

%U 165,2,171,179,89,177,184,191,49,201,199,101,207,208,43,109,55,227,2,233,119

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

%H G. C. Greubel, <a href="/A161867/b161867.txt">Table of n, a(n) for n = 1..1000</a>

%F 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.

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

%t 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)

%Y Cf. A161865, numerators for this sequence.

%K nonn,frac

%O 1,1

%A _Daniel Tisdale_, Jun 20 2009

%E Keyword:frac added by _R. J. Mathar_, Jun 30 2009

%E Extended beyond a(9) by _R. J. Mathar_, Sep 27 2009