Search: id:A156874
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%I A156874
%S A156874 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,
%T A156874 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,
%U A156874 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
%N A156874 Number of Sophie Germain primes <= n.
%C A156874 a(n) = SUM(A156660(k): 1<=k<=n);
%C A156874 a(n) = A156875(2*n+1);
%C A156874 Hardy-Littlewood conjecture: a(n) ~ 2*C2*n/(ln(n))^2, where C2=0.6601618158... 
               is the twin prime constant (see A005597).
%C A156874 The truth of the above conjecture would imply that there is an infinity 
               of Sophie Germain primes (which is also conjectured.)
%C A156874 a(n) ~ 2*C2*n/(ln(n))^2 is also conjectured by Hardy-Littlewood for the 
               number of twin primes <= n.
%H A156874 R. Zumkeller, <a href="b156874.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A156874 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sophie_Germain_prime">
               Sophie Germain prime</a>
%e A156874 a(120) = #{2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113} = 11.
%Y A156874 A156875, A156876, A156877, A156878, A000720.
%Y A156874 Cf. A005384 Sophie Germain primes p: 2p+1 is also prime.
%Y A156874 Sequence in context: A084506 A071578 A157791 this_sequence A078767 A093125 
               A156081
%Y A156874 Adjacent sequences: A156871 A156872 A156873 this_sequence A156875 A156876 
               A156877
%K A156874 nonn
%O A156874 1,3
%A A156874 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 18 2009
%E A156874 Edited and commented by Daniel Forgues (squid(AT)zensearch.com), Jul 
               31 2009

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