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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 (list; graph; refs; listen; history; text; internal format)
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

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; i-L>m&&m=i-L; 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

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Last modified June 2 11:20 EDT 2020. Contains 334771 sequences. (Running on oeis4.)