A176875 Numbers that are the product of two distinct primes a and b, such that a+b are averages of twin prime pairs.

35, 65, 77, 161, 185, 209, 221, 335, 341, 371, 377, 437, 485, 515, 611, 671, 707, 731, 767, 779, 851, 899, 917, 965, 1007, 1067, 1115, 1157, 1211, 1247, 1271, 1337, 1385, 1397, 1529, 1535, 1577, 1631, 1691, 1781, 1817, 1841, 1991, 2117, 2171, 2201, 2285

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2010

Keywords

• nonn

Examples

			35 = 5*7 is a term since 5 + 7 +- 1 are twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006881, A014574.

Programs

Mathematica

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
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 *)