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Maximal gap between quadratic residues mod n; here quadratic residues must be coprime to n.
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%I #15 Oct 10 2019 10:21:46

%S 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,

%T 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,

%U 10,6,48,7,10,12,8,13,24,7,16,18,20,8,24,5,10

%N Maximal gap between quadratic residues mod n; here quadratic residues must be coprime to n.

%C 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.

%D 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.]

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 45.

%D G. B. Mathews, Theory of Numbers, 2nd edition. Chelsea, NY, p. 32. [Does not require gcd(q,n)=1.]

%D 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.]

%D J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 270. [Does not require gcd(q,n)=1.]

%H David W. Wilson, <a href="/A248376/b248376.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/QuadraticResidue.html">MathWorld: Quadratic Residue</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Quadratic_residue">Quadratic residue</a>

%o (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}

%Y Cf. A063987, A130290, A088190, A088191, A088192, A248222.

%K nonn

%O 1,2

%A _David W. Wilson_ and _M. F. Hasler_, Oct 05 2014