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A176875
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Numbers that are the product of two distinct primes a and b, such that a+b are averages of twin prime pairs.
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7
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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35 = 5*7 is a term since 5 + 7 +- 1 are twin primes.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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