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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A006881, A014574.

Sequence in context: A092256 A108172 A354502 * A292005 A338008 A331378

Adjacent sequences: A176872 A176873 A176874 * A176876 A176877 A176878

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2010

Status

approved