A243867 Sum of the numbers N*(n) and N**(n) in A242974.
1, 7, 97, 1289, 20611, 365775, 7813466, 212149365
Offset: 3
Links
- V. Shevelev, Theorems on twin primes-dual case, arXiv:0912.4006 (Sections 10,14)
Formula
Let B(n) be the number of twin primes pairs not exceeding the n-th primorial M_n = A002110(n). Then we know that B(n) = O(M_n/(log(M_n))^2) = o(M_n/log((p_(n-1)))^2. For sufficiently large n, a(n) + B(n) >= 0.416...*M_n/(log(prime(n-1)))^2 (cf. Shevelev link) and thus for large n, for example, we have a(n) >= 0.4*M_n/(log(prime(n-1)))^2.
Extensions
More terms from Peter J. C. Moses, Jun 13 2014