A020649 - OEIS

%I #34 May 16 2022 22:18:41

%S 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,

%T 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,

%U 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

%N Least quadratic nonresidue modulo n (with n >= 3).

%C 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^((p-1)/2) == -1 (mod p), see A053760. - _Thomas Ordowski_, Apr 24 2019

%H Amiram Eldar, <a href="/A020649/b020649.txt">Table of n, a(n) for n = 3..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuadraticNonresidue.html">Quadratic Nonresidue</a>

%F a(prime(n)) = A053760(n) for n > 1. - _Thomas Ordowski_, Apr 24 2019

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

%o (PARI) residue(n,m)={local(r);r=0;for(i=0,floor(m/2),if(i^2%m==n,r=1));r}

%o 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

%Y Cf. A053760.

%K nonn

%O 3,1

%A _David W. Wilson_