A243867 Sum of the numbers N*(n) and N**(n) in A242974.

1, 7, 97, 1289, 20611, 365775, 7813466, 212149365

Offset

3,2

Links

Table of n, a(n) for n=3..10.

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.

Crossrefs

Cf. A242974, A242719, A242720, A242758, A243803, A243804.

Sequence in context: A093172 A074110 A155644 * A232290 A011943 A370101

Adjacent sequences: A243864 A243865 A243866 * A243868 A243869 A243870

Keyword

nonn,more

Author

Vladimir Shevelev, Jun 13 2014

Extensions

More terms from Peter J. C. Moses, Jun 13 2014

Status

approved