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A153439
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Numbers n such that n^6 + n^3 + 1 is prime
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3
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1, 2, 3, 8, 11, 20, 21, 26, 30, 50, 51, 56, 60, 78, 98, 102, 117, 129, 134, 146, 159, 171, 186, 189, 191, 198, 200, 209, 210, 212, 222, 240, 249, 267, 269, 278, 279, 299, 300, 333, 344, 363, 383, 390, 398, 399, 425, 429, 438, 444, 450, 458, 504, 509, 533, 540
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| n^6+n^3+1 is the cyclotomic polynomial Phi(9,n). Damianou, p.4, claims that there is strong experimental evidence that a(n) is prime for infinitely many values of n. Damianou gives a formula that precisely determines the cyclotomic factors of x^2n + x^n + 1, applicable to a(n) = n^6 + n^3 + 1. Jonathan Vos Post, Jan 06 2011
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LINKS
| Pierre CAMI, Table of n, a(n) for n=1,...,37835
Pantelis A. Damianou, On prime values of cyclotomic polynomials, Jan 06 2011.
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PROG
| (MAGMA) [n: n in [0..500] | IsPrime(n^3*(n^3+1)+1)] [From Vincenzo Librandi, Nov 26 2010]
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CROSSREFS
| Cf. A153438, A164989.
Sequence in context: A007676 A042443 A042263 * A119064 A048788 A143914
Adjacent sequences: A153436 A153437 A153438 * A153440 A153441 A153442
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KEYWORD
| nonn,changed
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AUTHOR
| Pierre CAMI (pierre-cami(AT)bbox.fr), Dec 26 2008
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EXTENSIONS
| I deleted some unclear comments. - N. J. A. Sloane, Sep 06 2009
More terms from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 25 2010
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