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%I #10 Jan 23 2015 16:10:21
%S 3,5,29,71,107,191,239,569,881,1091,1289,1619,1721,1931,1997,2081,
%T 2087,2129,2309,2381,2549,2591,2729,3299,3359,3527,3851,4229,4241,
%U 4271,4649,5279,5501,5651,6299,7127,7349,7547,7589,7757,8219,8969,9437,10037
%N a(n) = p, the lesser of twin primes (p, q=p+2) such that p*q - p - q is prime.
%C Or, p prime such that p+2 and p^2-2 are primes.
%H Harvey P. Dale, <a href="/A128551/b128551.txt">Table of n, a(n) for n = 1..1000</a>
%e 3, 5 and 3*5-3-5=7 are prime; 5, 7 and 5*7-5-7=23 are prime; 29, 31 and 29*31-29-31=839 are primes.
%t Clear[lst,f1,f2,n,p]; f1[n_]:=PrimeQ[n+2]; f2[n_]:=PrimeQ[n*(n+2)-((n+2)+n)]; lst={};Do[p=Prime[n];If[f1[p]&&f2[p],AppendTo[lst,p]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 19 2009 *)
%t tpQ[{a_,b_}]:=b-a==2&&PrimeQ[a*b-a-b]; Transpose[Select[Partition[ Prime[ Range[ 1300]],2,1],tpQ]][[1]] (* _Harvey P. Dale_, May 22 2014 *)
%Y Cf. A096342, A126148, A128547, A128548, A128550.
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 10 2007