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Search: id:A072226
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| A072226 |
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Values of n for which Phi_n(2) is prime, where Phi_n is the n-th cyclotomic polynomial. |
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4
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| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 22, 24, 26, 27, 30, 31, 32, 33, 34, 38, 40, 42, 46, 49, 56, 61, 62, 65, 69, 77, 78, 80, 85, 86, 89, 90, 93, 98, 107, 120, 122, 126, 127, 129, 133, 145, 150, 158, 165, 170, 174, 184, 192, 195, 202, 208, 234, 254, 261
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Numbers n for which A019320(n) is prime. The prime n in this sequence are in A000043, which produce the Mersenne primes. If 2p is in this sequence, with p prime, then p is a Wagstaff number, A000978. - T. D. Noe, Apr 02 2008
While the sequence looks quite dense for small values, note that there are only 10 values in the interval [700,1200]. - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 03 2008
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REFERENCES
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Yves Gallot, Cyclotomic polynomials and prime numbers (November 12, 2000; revised January 5, 2001)
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..277 (initial 234 terms from Yves Gallot)
Joerg Arndt, Fxtbook
Yves Gallot, Cyclotomic polynomials and prime numbers
Index entries for cyclotomic polynomials, values at X
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MATHEMATICA
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Select[Range[600], PrimeQ[Cyclotomic[ #, 2]]&]
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PROGRAM
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(PARI) for( i=1, 999, ispseudoprime( polcyclo(i, 2)) && print1( i", ")) /* for PARI < 2.4.2 use ...subst(polcyclo(i), x, 2)... */ - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 03 2008
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CROSSREFS
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Cf. A138920-A138940.
Sequence in context: A102823 A004775 A004744 this_sequence A074402 A094270 A125705
Adjacent sequences: A072223 A072224 A072225 this_sequence A072227 A072228 A072229
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KEYWORD
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nonn
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AUTHOR
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Reiner Martin (reinermartin(AT)hotmail.com), Jul 04 2002
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