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A128852
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Anti-elite primes: a prime number p is called anti-elite if only a finite number of Fermat numbers 2^(2^n)+1 are quadratic non-residues mod p.
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1
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2, 13, 17, 97, 193, 241, 257, 641, 673, 769, 2689, 5953, 8929, 12289, 40961, 49921, 61681, 65537, 101377, 114689, 274177, 286721, 319489, 414721, 417793, 550801, 786433, 974849, 1130641, 1376257, 1489153, 1810433, 2424833, 3602561, 6700417
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| There are infinitely many anti-elite primes.
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REFERENCES
| Alexander Aigner; Ueber Primzahlen, nach denen (fast) alle Fermatzahlen quadratische Nichtreste sind. Monatsh. Math. 101 (1986), pp. 85-93
T. Mueller, On anti-elite prime numbers, Journal of Integer Sequences, 10 (2007), Article 07.9.4 [From Tom Mueller (muel4503(AT)uni-trier.de), Dec 30 2008]
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LINKS
| Dennis Martin, Table of n, a(n) for n = 1..101
Dennis Martin, Anti-Elite Prime Search [From Dennis Martin (dennis.martin(AT)dptechnology.com), Dec 18 2008]
Tom Mueller, On Anti-Elite Prime Numbers, J. Integer Sequences, Vol. 10 (2007), Article 07.9.4. [From Dennis Martin (dennis.martin(AT)dptechnology.com), Jan 17 2009]
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EXAMPLE
| Let F_r:=2^(2^r)+1 = r-th Fermat number. Then a(2)=13 because for all r>1 we have F_r == 4 (mod 13) if r is even, resp. F_r == 10 (mod 13) if r is odd. Notice that 4 and 10 are quadratic residues modulo 13.
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CROSSREFS
| Cf. A102742.
Sequence in context: A109181 A175448 A067522 * A191765 A063615 A020585
Adjacent sequences: A128849 A128850 A128851 * A128853 A128854 A128855
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KEYWORD
| nonn
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AUTHOR
| Tom Mueller (muel4503(AT)uni-trier.de), Apr 16 2007
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