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A178337
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Numbers k such that (k^3 + 2, n^3 + 4) is a twin prime pair.
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5
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1, 3, 45, 63, 69, 129, 363, 495, 555, 579, 885, 993, 1053, 1185, 1719, 1839, 2055, 2175, 2199, 2409, 2595, 3039, 3063, 3303, 3399, 3555, 3615, 4245, 4443, 4449, 5073, 5373, 5535, 5703, 5949, 6015, 6075, 6693, 6795, 6849, 7023, 7119, 7155, 7509, 7779, 8535
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OFFSET
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1,2
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COMMENTS
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With the exception of k = 1, all k are odd multiples of 3 with a least-significant decimal digit of 3, 5 or 9.
A178336(n) gives the values of k^3 + 2.
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LINKS
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EXAMPLE
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1^3 + 2 = 3 = prime(2) and 3+2 = prime(3) are twin primes, so n=1 is a term.
45^3 + 2 = 91127 = prime(8811) and 91127+2 = prime(8812) are twin primes, so 45 is a term.
10893^3 + 2 = 1292535591959 = prime(48144179941) is a lower twin prime, so 10893 is a term.
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MATHEMATICA
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seqQ[n_] := And @@ PrimeQ[n^3 + 3 + {-1, 1}]; Select[Range[8535], seqQ] (* Amiram Eldar, Jan 11 2020*)
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PROG
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(Magma) [n: n in [0..9000] | IsPrime(n^3+2) and IsPrime(n^3+4)]; // Vincenzo Librandi, Nov 18 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 25 2010
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EXTENSIONS
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STATUS
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approved
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