

A020649


Least quadratic nonresidue of n.


7



2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 5, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 2, 2, 5, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2
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OFFSET

3,1


COMMENTS

a(n) is the smallest q such that the congruence x^2 == q (mod n) has no solution 0 < x < n, for n > 2. Note that a(n) is a prime. If n is an odd prime p, then a(p) is the smallest base b such that b^((p1)/2) == 1 (mod p), see A053760.  Thomas Ordowski, Apr 24 2019


LINKS

Table of n, a(n) for n=3..110.
Eric Weisstein's World of Mathematics, Quadratic Nonresidue


FORMULA

a(prime(n)) = A053760(n) for n > 1.  Thomas Ordowski, Apr 24 2019


PROG

(PARI) residue(n, m)={local(r); r=0; for(i=0, floor(m/2), if(i^2%m==n, r=1)); r}
A020649(n)={local(r, m); r=0; m=0; while(r==0, m=m+1; if(!residue(m, n), r=1)); m} \\ Michael B. Porter, Apr 30 2010


CROSSREFS

Cf. A053760.
Sequence in context: A231727 A270616 A304523 * A183024 A067131 A094915
Adjacent sequences: A020646 A020647 A020648 * A020650 A020651 A020652


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



