%I
%S 2,3,5,7,13,23,31,113,1327,31397,370261,492113,2010733,20831323,
%T 25056082087,42652618343,2614941710599,19581334192423
%N Primes prime(n) such that prime(n+1)  prime(n) > log(n)^2.
%C Using terms of A002386, a(19) is probably 218209405436543.  _T. D. Noe_, Apr 24 2012
%t t = {}; Do[If[Prime[n + 1]  Prime[n] > Log[n]^2, AppendTo[t, Prime[n]]], {n, 10000}]; t (* _T. D. Noe_, Apr 24 2012 *)
%o (PARI) n=0;G=1;p=2;forprime(q=3,1e8,n++;if(qp>=G&&qp>log(n)^2, G=ceil(log(n)^2);print1(p", "));p=q) \\ _Charles R Greathouse IV_, Apr 24 2012
%Y Subsequence of A211073.
%Y Cf. A002386, A134266.
%K nonn,hard,more
%O 1,1
%A _Thomas Ordowski_, Apr 24 2012
%E a(13)a(16) from _Charles R Greathouse IV_, Apr 24 2012
%E a(17) from _Charles R Greathouse IV_, Apr 26 2012
%E a(18) from _Charles R Greathouse IV_, May 06 2012
