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A154669
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Averages of twin prime pairs n such that 2*n^3+12*n^2 is a square.
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0
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12, 282, 642, 1452, 12162, 17292, 34842, 98562, 194682, 233922, 347772, 383682, 410412, 544962, 749082, 1071642, 1302492, 1421292, 1503372, 1685442, 2794242, 3011052, 3235962, 3312732, 3792252, 3875322, 4755522
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 11,12,13;Sqrt[2*12^3+12*12^2]=72,...
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MAPLE
| a := proc (n) if isprime(n-1) = true and isprime(n+1) = true and type(sqrt(2*n^3+12*n^2), integer) = true then n else end if end proc: seq(a(n), n = 3 .. 5000000); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 20 2009]
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MATHEMATICA
| a[n_]:=Sqrt[2*n^3+12*n^2]; lst={}; Do[If[Floor[a[n]]==a[n], If[PrimeQ[n-1]&&PrimeQ[n+1], AppendTo[lst, n]]], {n, 9!}]; lst
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CROSSREFS
| Cf. A152811
Sequence in context: A166337 A183767 A009604 * A079519 A077424 A159827
Adjacent sequences: A154666 A154667 A154668 * A154670 A154671 A154672
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KEYWORD
| nonn
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 13 2009
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EXTENSIONS
| Extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 20 2009
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