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Search: id:A156874
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| A156874 |
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Number of Sophie Germain primes <= n. |
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+0
7
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| 0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) = SUM(A156660(k): 1<=k<=n);
a(n) = A156875(2*n+1);
Hardy-Littlewood conjecture: a(n) ~ 2*C2*n/(ln(n))^2, where C2=0.6601618158... is the twin prime constant (see A005597).
The truth of the above conjecture would imply that there is an infinity of Sophie Germain primes (which is also conjectured.)
a(n) ~ 2*C2*n/(ln(n))^2 is also conjectured by Hardy-Littlewood for the number of twin primes <= n.
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
Wikipedia, Sophie Germain prime
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EXAMPLE
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a(120) = #{2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113} = 11.
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CROSSREFS
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A156875, A156876, A156877, A156878, A000720.
Cf. A005384 Sophie Germain primes p: 2p+1 is also prime.
Sequence in context: A084506 A071578 A157791 this_sequence A078767 A093125 A156081
Adjacent sequences: A156871 A156872 A156873 this_sequence A156875 A156876 A156877
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 18 2009
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EXTENSIONS
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Edited and commented by Daniel Forgues (squid(AT)zensearch.com), Jul 31 2009
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