cp's OEIS Frontend

A309129 Numbers n such that -n is a quadratic nonresidue modulo all odd primes p <= sqrt(n) which do not divide n.

%I A309129 #25 Jul 26 2019 18:29:24
%S A309129 1,2,3,4,5,6,7,8,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,33,37,40,
%T A309129 42,43,45,48,57,58,60,63,67,70,72,78,85,88,93,100,102,105,112,120,130,
%U A309129 133,135,147,148,163,165,168,177,190,210,232,240,247,253,267,268,273,280,312,330,333,345,357,385,408,462,520,522,652,708,760,840,928,1320,1365,1467,1848
%N A309129 Numbers n such that -n is a quadratic nonresidue modulo all odd primes p <= sqrt(n) which do not divide n.
%C A309129 Contains A000926 and A003173 (except the term 11) as subsequences.
%C A309129 Conjecture: 1848 is the last term of this sequence.
%e A309129 42 is in this sequence because sqrt(42) = 6.480740..., and -42 is quadratic nonresidue mod all odd primes < 6.480740... not dividing 42 (only mod 5).
%e A309129 67 is in this sequence because sqrt(67) = 8.185352..., and -67 is quadratic nonresidue mod all odd primes < 8.185352... not dividing 67 (mod 3, mod 5 and mod 7).
%e A309129 17 is not in this sequence because -17 is quadratic residue mod 3 and 3 < sqrt(17) and 3 does not divide 17.
%e A309129 90 is not in this sequence because -90 is quadratic residue mod 7 and 7 < sqrt(90) and 7 does not divide 90.
%e A309129 For n < 9, the range of p is empty, thus the numbers n < 9 are trivially in this sequence.
%o A309129 (PARI) a(n)=forprime(p=3, ,if(kronecker(-n,p)==1,return(p)))
%o A309129 for(k=1, 10^6,if(a(k)>sqrt(k),print1(k, ", ")))
%Y A309129 Cf. A000926, A003173.
%K A309129 nonn
%O A309129 1,2
%A A309129 _Richard N. Smith_, Jul 13 2019