%I #4 May 12 2016 09:03:57
%S 43,863,1181,3467,10613,23081,26189,27803,42407,138731,463949,630167,
%T 702101,1038731,1417649,1452851,2005061,2060921,4925861,6565721,
%U 9709163,9739721,10047881,14268113,15515573,16575113,16615031,17300873,17382461
%N Primes of the Form : p1=a*b+c;p2=a*c+b;p3=b*c+a;p=(p1+p2+p3)/2; p1,p2 and p3 are three consecutive prime numbers.
%H Harvey P. Dale, <a href="/A157722/b157722.txt">Table of n, a(n) for n = 1..1000</a>
%t lst={};Do[a=Prime[n];b=Prime[n+1];c=Prime[n+2];x=a*b+c;y=a*c+b;z=b*c+a;p=(x+y+z)/2;If[PrimeQ[p],AppendTo[lst,p]],{n,1,7!}];lst
%t prf[{a_,b_,c_}]:=Module[{x=a*b+c,y=b*c+a,z=a*c+b,k},k=(x+y+z)/2;If[PrimeQ[ k], k,0]]; DeleteCases[prf/@Partition[Prime[Range[500]],3,1],0] (* _Harvey P. Dale_, May 12 2016 *)
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 04 2009