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 A156874 Number of Sophie Germain primes <= n. 12
 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; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) = Sum_{k=1..n} A156660(k). a(n) = A156875(2*n+1). Hardy-Littlewood conjecture: a(n) ~ 2*C2*n/(log(n))^2, where C2=0.6601618158... is the twin prime constant (see A005597). The truth of the above conjecture would imply that there exists an infinity of Sophie Germain primes (which is also conjectured). a(n) ~ 2*C2*n/(log(n))^2 is also conjectured by Hardy-Littlewood for the number of twin primes <= n. LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Sophie Germain prime Wikipedia, Sophie Germain prime FORMULA a(10^n)= A092816(n). - Enrique Pérez Herrero, Apr 26 2012 EXAMPLE a(120) = #{2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113} = 11. MATHEMATICA Accumulate[Table[Boole[PrimeQ[n]&&PrimeQ[2n+1]], {n, 1, 200}]] (* Enrique Pérez Herrero, Apr 26 2012 *) CROSSREFS A156875, A156876, A156877, A156878, A000720. Cf. A005384 Sophie Germain primes p: 2p+1 is also prime. Cf. A092816. Sequence in context: A071578 A157791 A236857 * A294234 A078767 A331137 Adjacent sequences:  A156871 A156872 A156873 * A156875 A156876 A156877 KEYWORD nonn AUTHOR Reinhard Zumkeller, Feb 18 2009 EXTENSIONS Edited and commented by Daniel Forgues, Jul 31 2009 STATUS approved

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Last modified April 10 07:44 EDT 2021. Contains 342843 sequences. (Running on oeis4.)