The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #2 Mar 31 2012 12:38:31
%S 1,3,10,13,14,20,30,34,40,44,110,129,135,139,154,175,188,220,229,238,
%T 273,315,405,413,440,464,465,503,520,560,569,579,583,590,685,688,695,
%U 758,833,835,859,868,903,959,1025,1158,1378,1538,1613,1624,1659,1669
%N Least of 3 consecutive integers such that product of them is average of twin prime pairs.
%C 1*2*3=6+-1 -> primes, 3*4*5=60+-1 -> primes,...
%t f1[n_]:=PrimeQ[n-1]&&PrimeQ[n+1];f2[n_]:=n*(n+1)*(n+2);lst={};Do[If[f1[f2[n]],AppendTo[lst,n]],{n,8!}];lst
%Y Cf. A014574
%K nonn
%O 1,2
%A _Vladimir Joseph Stephan Orlovsky_, Mar 13 2010