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Search: id:A140114
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| A140114 |
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Number of semiprimes strictly between n^2 and (n+1)^2. |
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+0
2
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| 0, 0, 1, 3, 2, 4, 3, 5, 4, 8, 5, 8, 7, 6, 13, 7, 7, 13, 10, 12, 9, 14, 14, 15, 11, 12, 18, 16, 16, 17, 18, 15, 16, 20, 20, 21, 22, 21, 18, 19, 21, 24, 24, 23, 25, 23, 29, 21, 23, 31, 29, 23, 21, 30, 33, 35, 34, 27, 30, 28, 29, 32, 30, 31, 36, 36, 36, 36, 36, 43, 24, 40, 38, 40, 39
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Can it be proved that a(n)>0 for n>1?
Chen proves that there is a semiprime between n^2 and (n+1)^2 for sufficiently large n. [From T. D. Noe (noe(AT)sspectra.com), Oct 17 2008]
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REFERENCES
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Jing Run Chen, On the distribution of almost primes in an interval, Sci. Sinica 18 (1975), 611-627. [From T. D. Noe (noe(AT)sspectra.com), Oct 17 2008]
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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EXAMPLE
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The first semiprimes are 6,10,14,15,21,22,26
None is <4, hence a(0)=a(1)=0
One only is <9, hence a(2) = 1
Three more, 10, 14, 15 are <16, hence a(3)=3
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MATHEMATICA
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SemiPrimeQ[n_] := TrueQ[Plus@@Last/@FactorInteger[n]==2]; Table[Length[Select[Range[n^2+1, n^2+2n], SemiPrimeQ]], {n, 0, 100}] [From T. D. Noe (noe(AT)sspectra.com), Sep 25 2008]
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CROSSREFS
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Cf. A014085
Sequence in context: A007456 A119707 A052938 this_sequence A025532 A133131 A026923
Adjacent sequences: A140111 A140112 A140113 this_sequence A140115 A140116 A140117
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KEYWORD
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easy,nonn
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AUTHOR
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Philippe Lallouet (philip.lallouet(AT)orange.fr), May 08 2008
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EXTENSIONS
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Corrected, edited and extended by T. D. Noe (noe(AT)sspectra.com), Sep 25 2008
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