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A248376
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Maximal gap between quadratic residues mod n; here quadratic residues must be coprime to n.
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2
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1, 2, 3, 4, 3, 6, 4, 8, 3, 8, 4, 12, 5, 8, 12, 8, 4, 6, 5, 12, 12, 8, 6, 24, 3, 8, 3, 16, 4, 18, 5, 8, 12, 8, 13, 12, 5, 10, 15, 32, 6, 24, 6, 16, 12, 12, 6, 24, 4, 8, 18, 20, 7, 6, 13, 32, 15, 10, 6, 48, 7, 10, 12, 8, 13, 24, 7, 16, 18, 20, 8, 24, 5, 10
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OFFSET
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1,2
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COMMENTS
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The definition of quadratic residue modulo a nonprime varies from author to author. Sometimes, quadratic residues are not required to be coprime to n, cf. A248222 for the corresponding variant of this sequence.
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REFERENCES
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K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer, 1982, p. 194. [Requires gcd(q,n)=1 for q to be a quadratic residue mod n.]
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 45.
G. B. Mathews, Theory of Numbers, 2nd edition. Chelsea, NY, p. 32. [Does not require gcd(q,n)=1.]
Ivan Niven and Herbert S. Zuckerman, An Introduction to the Theory of Numbers, New York: John Wiley, 2nd ed., 1966, p. 69. [Requires gcd(q,n)=1 for q to be a quadratic residue mod n.]
J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 270. [Does not require gcd(q,n)=1.]
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LINKS
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PROG
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(PARI) a(n)={L=m=1; for(i=2, n+1, gcd(i, n)>1&&next; issquare(Mod(i, n))||next; i-L>m&&m=i-L; L=i); m}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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