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A248376
Maximal gap between quadratic residues mod n; here quadratic residues must be coprime to n.
2
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
OFFSET
1,2
COMMENTS
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.
REFERENCES
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.]
LINKS
PROG
(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}
CROSSREFS
KEYWORD
nonn
AUTHOR
David W. Wilson and M. F. Hasler, Oct 05 2014
STATUS
approved