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Search: id:A108701
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| A108701 |
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Values of n such that n^2-2 and n^2+2 are both prime. |
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+0
6
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| 3, 9, 15, 21, 33, 117, 237, 273, 303, 309, 387, 429, 441, 447, 513, 561, 573, 609, 807, 897, 1035, 1071, 1113, 1143, 1233, 1239, 1311, 1563, 1611, 1617, 1737, 1749, 1827, 1839, 1953, 2133, 2211, 2283, 2589, 2715, 2721, 2955, 3081, 3093, 3453, 3549, 3555
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Since x^2+2 is divisible by 3 unless x is divisible by 3, all elements are 3 mod 6.
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REFERENCES
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Beauregard, R.A. and Suryanarayan, E.R. Square-plus-two primes, Mathematical Gazette 85(502) 90-1
David Wells, Prime Numbers, John Wiley and Sons, 2005, p. 219 (article:'Siamese primes')
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EXAMPLE
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21 is on the list since 21^2-2=439 and 21^2+2=443 are primes.
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MATHEMATICA
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a[n_]:=n^x-y; b[n_]:=n^x+y; lst={}; x=2; y=2; Do[If[PrimeQ[a[n]]&&PrimeQ[b[n]], AppendTo[lst, n]], {n, 0, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
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CROSSREFS
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Cf. A028870, A028873, A038599, A153974 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
Sequence in context: A071526 A114271 A137164 this_sequence A064539 A029482 A139419
Adjacent sequences: A108698 A108699 A108700 this_sequence A108702 A108703 A108704
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KEYWORD
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nonn
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AUTHOR
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John L. Drost (drost(AT)marshall.edu), Jun 19 2005
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