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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 18 2009
EXTENSIONS
Edited and commented by Daniel Forgues, Jul 31 2009
STATUS
approved