

A020649


Least quadratic nonresidue of n.


17



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

Amiram Eldar, Table of n, a(n) for n = 3..10000
Eric Weisstein's World of Mathematics, Quadratic Nonresidue


FORMULA

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


MATHEMATICA

a[n_] := Min @ Complement[Range[n  1], Mod[Range[n/2]^2, n]]; Table[a[n], {n, 3, 110}] (* Amiram Eldar, Oct 29 2020 *)


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



