

A309129


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


0



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, 42, 43, 45, 48, 57, 58, 60, 63, 67, 70, 72, 78, 85, 88, 93, 100, 102, 105, 112, 120, 130, 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
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OFFSET

1,2


COMMENTS

Conjecture: 1848 is the last term of this sequence.


LINKS



EXAMPLE

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).
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).
17 is not in this sequence because 17 is quadratic residue mod 3 and 3 < sqrt(17) and 3 does not divide 17.
90 is not in this sequence because 90 is quadratic residue mod 7 and 7 < sqrt(90) and 7 does not divide 90.
For n < 9, the range of p is empty, thus the numbers n < 9 are trivially in this sequence.


PROG

(PARI) a(n)=forprime(p=3, , if(kronecker(n, p)==1, return(p)))
for(k=1, 10^6, if(a(k)>sqrt(k), print1(k, ", ")))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



