A006880(n)=number of primes < 10^n, A007508(n)=number of twin primes < 10^n. Let F(n) = A006880(n)/A007508(n). For n >3, we find that F(n) is ~ 0.762373*log(10^n) - 0.968855.
Let FF(n) = A006880(n)/a(n). For n>3, we find that FF(n) is ~ 0.163128*log(10^n) + 1.349255. a(n)/A007508(n) is then ~ 0.762373*log((10^n) - 0.968855 / ( 0.163128*log(10^n) + 1.349255, as n tends to infinity a(n)/ A007508(n) needs to tend to 0.762373 / 0.163128 = 4.673465.
