%I A153414
%S A153414 5,7,31,61,139,181,241,421,619,1051,1609,1699,1789,2269,2311,2731,3259,
%T A153414 3391,3529,3769,4159,4219,4339,4801,5641,5869,6661,6691,6871,6961,7489,
%U A153414 7549,7591,8539,8629,8971,9631,9859,9931,10459,11119,11971,12541,13339
%N A153414 Larger of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.
%C A153414 3*5+4=19 prime, 5*7+6=41 prime, 29*31+30=929 prime, ...
%t A153414 lst={};Do[p1=Prime[n];p2=Prime[n+1];If[p2-p1==2,a=p1*p2+(p1+1);If[PrimeQ[a],
               AppendTo[lst,p2]]],{n,7!}];lst
%Y A153414 Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, 
               A153407, A153408, A153409, A153410, A153413
%Y A153414 Sequence in context: A025095 A025114 A090935 this_sequence A104815 A007911 
               A066172
%Y A153414 Adjacent sequences: A153411 A153412 A153413 this_sequence A153415 A153416 
               A153417
%K A153414 nonn
%O A153414 1,1
%A A153414 Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 25 2008