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%I #9 Jan 02 2020 04:15:51
%S 35,65,77,161,185,209,221,335,341,371,377,437,485,515,611,671,707,731,
%T 767,779,851,899,917,965,1007,1067,1115,1157,1211,1247,1271,1337,1385,
%U 1397,1529,1535,1577,1631,1691,1781,1817,1841,1991,2117,2171,2201,2285
%N Numbers that are the product of two distinct primes a and b, such that a+b are averages of twin prime pairs.
%H Amiram Eldar, <a href="/A176875/b176875.txt">Table of n, a(n) for n = 1..10000</a>
%e 35 = 5*7 is a term since 5 + 7 +- 1 are twin primes.
%t l[n_]:=Last/@FactorInteger[n]; f[n_]:=First/@FactorInteger[n]; lst={};Do[If[l[n]=={1,1},a=f[n][[1]];b=f[n][[2]];If[PrimeQ[a+b-1]&&PrimeQ[a+b+1],AppendTo[lst,n]]],{n,0,7!}];lst
%t With[{nn=100},Take[Union[Times@@@Select[Subsets[Prime[Range[nn]],{2}], AllTrue[Total[#]+{1,-1},PrimeQ]&]],nn/2]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, May 09 2015 *)
%Y Cf. A006881, A014574.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Apr 27 2010