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Larger of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.
1

%I #6 Nov 21 2013 12:49:29

%S 5,7,31,61,139,181,241,421,619,1051,1609,1699,1789,2269,2311,2731,

%T 3259,3391,3529,3769,4159,4219,4339,4801,5641,5869,6661,6691,6871,

%U 6961,7489,7549,7591,8539,8629,8971,9631,9859,9931,10459,11119,11971,12541,13339

%N Larger of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.

%C 3*5+4=19 prime, 5*7+6=41 prime, 29*31+30=929 prime, ...

%H Harvey P. Dale, <a href="/A153414/b153414.txt">Table of n, a(n) for n = 1..1000</a>

%t 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

%t Transpose[Select[Select[Partition[Prime[Range[1600]],2,1],Last[#]- First[#] == 2&], PrimeQ[Times@@#+Mean[#]]&]][[2]] (* _Harvey P. Dale_, Jan 23 2012 *)

%Y Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408, A153409, A153410, A153413

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008