cp's OEIS Frontend

A306493 a(n) is the least number such that the n-th prime is the least coprime quadratic nonresidue modulo a(n).

%I A306493 #16 Mar 08 2019 23:41:35
%S A306493 3,4,6,22,118,479,262,3622,5878,18191,24022,132982,296278,366791,
%T A306493 1289738,4539478,6924458,13620602,32290442,175244281,86060762,
%U A306493 326769242,131486759,84286438,937435558
%N A306493 a(n) is the least number such that the n-th prime is the least coprime quadratic nonresidue modulo a(n).
%C A306493 Different from A000229 because here the non-coprime quadratic nonresidues are ignored. For example, a(2) = 4 because although 2 is a quadratic nonresidue modulo 4, it is not coprime to 4.
%e A306493 For k = 118 we have: 2 is not coprime to 118, 11^2 == 3 (mod 118), 51^2 == 5 (mod 118), 19^2 == 7 (mod 118) and 11 is a quadratic nonresidue modulo 118. For all k < 118, at least one of 2, 3, 5, 7 is coprime quadratic nonresidue modulo k, so a(5) = 118.
%o A306493 (PARI) b(p,k) = gcd(p,k)==1&&!issquare(Mod(p,k))
%o A306493 a(n) = my(k=1); while(sum(i=1,n-1,b(prime(i),k))!=0 || !b(prime(n),k), k++); k
%Y A306493 Cf. A000229.
%K A306493 nonn,more
%O A306493 1,1
%A A306493 _Jianing Song_, Feb 19 2019
%E A306493 a(17)-a(23) from _Daniel Suteu_, Feb 24 2019
%E A306493 a(24)-a(25) from _Jinyuan Wang_, Mar 08 2019