|
%I #8 Feb 14 2014 03:30:41
%S 0,1,3,2,3,2,2,2,2,1,1,2,3,2,1,1,1,1,1,1,2,1,3,3,2,3,2,1,2,1,2,1,2,3,
%T 2,2,1,3,3,4,4,4,3,4,1,1,3,3,2,3,1,1,2,2,4,1,4,3,5,4,5,4,3,4,3,4,3,2,
%U 1,4,3,4,6,1,3,3,3,4,2,3
%N a(n) = |{0 < k <= n: the number of Sophie Germain primes among 1, ..., k*n is a Sophie Germain prime}|.
%C Conjecture: a(n) > 0 for all n > 1.
%C See also A237839 for a similar conjecture involving twin primes.
%H Zhi-Wei Sun, <a href="/A237838/b237838.txt">Table of n, a(n) for n = 1..1000</a>
%e a(20) = 1 since 11 is a Sophie Germain prime, and there are exactly 11 Sophie Germain primes among 1, ..., 6*20 (namely, they are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113).
%t SG[n_]:=PrimeQ[n]&&PrimeQ[2n+1]
%t sg[n_]:=Sum[If[PrimeQ[2*Prime[k]+1],1,0],{k,1,PrimePi[n]}]
%t a[n_]:=Sum[If[SG[sg[k*n]],1,0],{k,1,n}]
%t Table[a[n],{n,1,80}]
%Y Cf. A005384, A237578, A237768, A237815, A237839.
%K nonn
%O 1,3
%A _Zhi-Wei Sun_, Feb 14 2014
|
