

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
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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 ErrorCorrecting Codes, ElsevierNorth 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, McGrawHill, NY, 1939, p. 270. [Does not require gcd(q,n)=1.]


LINKS

David W. Wilson, Table of n, a(n) for n = 1..10000
Eric W. Weisstein, MathWorld: Quadratic Residue
Wikipedia, Quadratic residue


PROG

(PARI) a(n)={L=m=1; for(i=2, n+1, gcd(i, n)>1&&next; issquare(Mod(i, n))next; iL>m&&m=iL; L=i); m}


CROSSREFS

Cf. A063987, A130290, A088190, A088191, A088192, A248222.
Sequence in context: A167234 A088043 A332931 * A138796 A186970 A064380
Adjacent sequences: A248373 A248374 A248375 * A248377 A248378 A248379


KEYWORD

nonn


AUTHOR

David W. Wilson and M. F. Hasler, Oct 05 2014


STATUS

approved



