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A153402
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Smaller of 3 consecutive prime numbers such that p1*p2*p3+d1+d2-1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.
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6
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3, 569, 1747, 5107, 6947, 9281, 11027, 14389, 24851, 25169, 26189, 31153, 34469, 41687, 42391, 45281, 61091, 62507, 80603, 82139, 89989, 91967, 92333, 93809, 98369, 98873, 103583, 105899, 111347, 117127, 120977, 122819, 128411, 135601
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OFFSET
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1,1
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COMMENTS
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3*5*7+2+2-1=108+-1=prime,
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LINKS
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MATHEMATICA
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lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; p3=Prime[n+2]; d1=p2-p1; d2=p3-p2; a=p1*p2*p3+d1+d2-1; If[PrimeQ[a-1]&&PrimeQ[a+1], AppendTo[lst, p1]], {n, 8!}]; lst
s3cpQ[{a_, b_, c_}]:=Module[{tp=a*b*c+(c-a)-1}, AllTrue[tp+{1, -1}, PrimeQ]]; Select[ Partition[Prime[Range[15000]], 3, 1], s3cpQ][[All, 1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 01 2018 *)
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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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