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Search: id:A053760
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| A053760 |
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Smallest positive quadratic nonresidue modulo p, where p is the n-th prime. |
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+0
5
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| 2, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 2, 2, 2, 7, 5, 3, 2, 3, 5, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 2, 7, 5, 2, 3, 2, 3, 2, 2, 3, 7, 7, 2, 3, 5, 2, 3, 2, 3, 2, 2, 2, 11, 5, 2, 2, 5, 2, 2, 3, 7, 3, 2, 2, 5, 2, 2, 3, 7, 2, 2, 7, 5, 3, 2, 3, 5, 2, 3, 2, 13, 3, 2, 2, 5, 2, 3, 2, 2, 2, 2, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Assuming the Generalized Riemann Hypothesis, Montgomery proved a(n) << (log p(n))^2, meaning that there is a constant c such that |a(n)| =< c*(log p(n))^2. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 06 2007
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REFERENCES
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R. Baillie and S. S. Wagstaff, Lucas pseudoprimes, Math. Comp. 35 (1980) 1391-1417; Math. Rev. 81j:10005.
P. Erdos, Remarks on number theory. I., Mat. Lapok 12 (1961) 10-17; Math. Rev. 26 #2410.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 94-98.
P. Ribenboim, The New Book of Prime Number Records, 3rd ed., Spinger-Verlag 1996; Math. Rev. 96k:11112.
H. L. Montgomery, Topics in Multiplicative Number Theory, 3rd ed., Lecture Notes in Mathematics, Vol. 227 (1971), MR 49:2616.
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LINKS
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S. R. Finch, Quadratic Residues
K. Matthews, Finding n(p), the least quaratic non-residue (mod p)
Eric Weisstein's World of Mathematics, Quadratic Nonresidue
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CROSSREFS
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Sequence in context: A085694 A160493 A091322 this_sequence A129654 A138789 A116504
Adjacent sequences: A053757 A053758 A053759 this_sequence A053761 A053762 A053763
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KEYWORD
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nonn
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AUTHOR
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S. R. Finch (Steven.Finch(AT)inria.fr), Apr 05 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 08 2000
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