cp's OEIS Frontend

A330404 Least nonsquare k that is a quadratic residue modulo n.

%I A330404 #25 Feb 18 2021 12:53:54
%S A330404 2,2,3,5,5,3,2,8,7,5,3,12,3,2,6,17,2,7,5,5,7,3,2,12,6,3,7,8,5,6,2,17,
%T A330404 3,2,11,13,3,5,3,20,2,7,6,5,10,2,2,33,2,6,13,12,6,7,5,8,6,5,3,21,3,2,
%U A330404 7,17,10,3,6,8,3,11,2,28,2,3,6,5,11,3,2,20,7,2,3,21
%N A330404 Least nonsquare k that is a quadratic residue modulo n.
%C A330404 a(n) >= n if and only if n is in A254328.
%C A330404 It seems that lim_{n->oo} a(n)/n = 0. Conjectured last term m such that a(m)/m >= 1/k, k = 1, 2, 3, ...: 16, 48, 240, 288, 720, 720, 720, 720, 1008, 1440, ...
%H A330404 Jianing Song, <a href="/A330404/b330404.txt">Table of n, a(n) for n = 1..10000</a>
%e A330404 k is a quadratic residue modulo 16 if and only if k == 0, 1, 4, 9 (mod 16). Since 0, 1, 4, 9 and 16 are squares, a(16) = 17.
%e A330404 k is a quadratic residue modulo 48 if and only if k == 0, 1, 4, 9, 16, 25, 33, 36 (mod 48). Since 0, 1, 4, 9, 16 and 25 are squares, a(48) = 33.
%e A330404 k is a quadratic residue modulo 720 if and only if k == 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 145, ..., 676 (mod 720). Since 0, 1, 4, ..., 144 are squares, a(720) = 145.
%o A330404 (PARI) a(n) = my(k=1); while(!issquare(Mod(k,n)) || issquare(k), k++); k
%Y A330404 A309680 is an alternate version.
%Y A330404 Cf. A254328, A330423.
%K A330404 nonn
%O A330404 1,1
%A A330404 _Jianing Song_, Dec 14 2019