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Search: id:A161865
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| A161865 |
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Numerators of ratio of nonprimes in a square interval to that of nonprimes in that interval and its successor. |
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+0
4
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| 1, 3, 5, 2, 1, 3, 12, 13, 1, 16, 19, 10, 22, 1, 25, 13, 30, 31, 33, 17, 18, 38, 41, 40, 43, 46, 47, 16, 51, 1, 53, 56, 19, 60, 61, 32, 66, 65, 68, 23, 18, 76, 25, 1, 78, 83, 1, 82, 89, 45, 88, 89, 95, 24, 100, 101, 49, 104, 103, 21, 55, 27, 112, 1, 115, 59, 1, 20, 21, 15, 64, 1
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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The limit of this sequence is 1/2, as can be shown by setting an increasing lower bound on the ratio of composites in successive square intervals.
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EXAMPLE
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First few terms are: 1/4,3/8,5/11,2/5,1/2,3/7,12/25,13/29
For n=1: there is 1 nonprime <=1, 2 nonprimes <=4, and 5 nonprimes <=9. The ratio is (2 - 1)/(5 - 1) = 1/4.
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MAPLE
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A062298 := proc(n) n-numtheory[pi](n) ; end: A078435 := proc(n) A062298(n^2) ; end: A161865 := proc(n) r := [ A078435(n), A078435(n+1), A078435(n+2)] ; (r[2]-r[1])/(r[3]-r[1]) ; numer(%) ; end: seq(A161865(n), n=1..120) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 27 2009]
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MATHEMATICA
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((2n+1)-(PrimePi[(n+1)^2]-PrimePi[n^2]))/((4n+4)-(PrimePi[(n+2)^2]-PrimePi[n^2])\ ), {n, 1, 40}]
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CROSSREFS
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Cf. A161621, A161622, A161867.
Sequence in context: A069111 A021288 A140735 this_sequence A145325 A126353 A094791
Adjacent sequences: A161862 A161863 A161864 this_sequence A161866 A161867 A161868
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KEYWORD
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nonn
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AUTHOR
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Daniel Tisdale (daniel6874(AT)gmail.com), Jun 20 2009
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EXTENSIONS
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Extended beyond a(8) by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 27 2009
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