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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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7
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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, Jan 06 2007
a(n) < 1 + sqrt(p), where p is the n-th prime (Theorem 3.9 in Niven, Zuckerman, and Montgomery). - Jonathan Sondow, May 13 2010
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REFERENCES
| 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.
Ivan Niven, Herbert S. Zuckerman, and Hugh L. Montgomery, An Introduction to the Theory Of Numbers, Fifth Edition, John Wiley and Sons, Inc., NY 1991, p. 147.
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LINKS
| S. R. Finch, Quadratic Residues
K. Matthews, Finding n(p), the least quadratic non-residue (mod p)
Eric Weisstein's World of Mathematics, Quadratic Nonresidue
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PROG
| (PARI) residue(n, m)={local(r); r=0; for(i=0, floor(m/2), if(i^2%m==n, r=1)); r
A053760(n)={local(r, m); r=0; m=0; while(r==0, m=m+1; if(!residue(m, prime(n)), r=1)); m} \\ Michael B. Porter, May 02 2010
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CROSSREFS
| Sequence in context: A103507 A085694 A160493 * A129654 A138789 A116504
Adjacent sequences: A053757 A053758 A053759 * A053761 A053762 A053763
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KEYWORD
| nonn
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AUTHOR
| S. R. Finch (Steven.Finch(AT)inria.fr), Apr 05 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 08 2000
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