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A152787
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Numbers k such that both k and k^2/2 are averages of twin prime pairs.
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3
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6, 12, 42, 72, 600, 642, 882, 2130, 2382, 2688, 3558, 3582, 4548, 6132, 7548, 8010, 9042, 13398, 13932, 15972, 17598, 19140, 21492, 26250, 26262, 34512, 38670, 39228, 39342, 48312, 49740, 52542, 53088, 53592, 55050, 55662, 56100, 56712, 65028, 65448, 65520
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OFFSET
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1,1
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LINKS
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FORMULA
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MATHEMATICA
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lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; If[p2-p1==2, e=(2*(p1+1))^(1/2); i=Floor[e]; If[e==i, If[PrimeQ[i-1]&&PrimeQ[i+1], AppendTo[lst, i]]]], {n, 10!}]; lst
Select[Mean/@Select[Partition[Prime[Range[10000]], 2, 1], #[[2]]-#[[1]] == 2&], And@@PrimeQ[#^2/2+{1, -1}]&](* Harvey P. Dale, May 12 2014 *)
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PROG
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(Magma) [2*k:k in [1..40000]| IsPrime(2*k-1) and IsPrime(2*k+1) and IsPrime(2*k^2 -1) and IsPrime(2*k^2 +1) ]; // Marius A. Burtea, Dec 31 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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