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A176875 Numbers that are the product of two distinct primes a and b, such that a+b are averages of twin prime pairs. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

35=5*7; 5+7+-1 -> primes,...

LINKS

Table of n, a(n) for n=1..47.

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: A245274 A092256 A108172 * A162832 A224485 A267330

Adjacent sequences:  A176872 A176873 A176874 * A176876 A176877 A176878

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 27 2010

STATUS

approved

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Last modified May 30 06:51 EDT 2017. Contains 287302 sequences.