login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Sum of the numbers N*(n) and N**(n) in A242974.
1

%I #23 Jun 23 2015 22:57:10

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

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

%H V. Shevelev, <a href="http://arXiv.org/abs/0912.4006">Theorems on twin primes-dual case</a>, arXiv:0912.4006 (Sections 10,14)

%F 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.

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

%K nonn,more

%O 3,2

%A _Vladimir Shevelev_, Jun 13 2014

%E More terms from _Peter J. C. Moses_, Jun 13 2014