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In case k is restricted to be a prime, the condition (p|k) = -1 becomes equivalent to say saying that p is a quadratic non-residue (mod k). - M. F. Hasler, Jan 18 2016
Least number k such that the first n primes are not squares mod have Kronecker symbol (p|k) = -1.
That This implies, but is, not equivalent to, that the first n primes are quadratic non-residues mod k. The first 13 terms are prime[Corrected by _M. Sequence A191089 is similar, but forces k to be primeF. Hasler_, Jan 18 2016]
The first 13 terms are prime. Sequence A191089 is similar, but forces k to be prime.
In case k is restricted to be a prime, the condition (p|k) = -1 becomes equivalent to say that p is a quadratic non-residue (mod k). - M. F. Hasler, Jan 18 2016
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a(1) = 3 is the least number k > 1 such that prime(1) = 2 is not a square mod k (since for k=1 and k=2, p=2 would be zero, thus a square, mod k).
a(2) = 4 is the least number > 1 k such that prime(1) = 2 and prime(2) = 3 are not squares mod p k (the only squares mod 4 are 0 = 0^1 = 2^2 and 1 = 1^2 = 3^3 (mod 4); while for k=2, p=2 would be zero, thus a square, and for k=3 this would be the case for p=3).
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a(1) = 3 is the least number k > 1 such that prime(1) = 2 is not a square mod k (since for k=1 and k=2, p=2 would be zero, thus a square, mod k).
a(2) = 4 is the least number > 1 such that 2 and 3 are not squares mod p (the only squares mod 4 are 0 = 0^1 = 2^2 and 1 = 1^2 = 3^3 (mod 4); while for k=2, p=2 would be zero, thus a square, and for k=3 this would be the case for p=3).
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(PARI) q=2; for(k=3, 1e9, forprime(p=2, q, if(kronecker(p, k)>=0, next(2))); print1(k", "); q=nextprime(q+1); k--) \\ _Charles R Greathouse IV, _, Oct 10 2011
a(16)-a(28) from _Charles R Greathouse IV, _, Oct 10 2011
_T. D. Noe (noe(AT)sspectra.com), _, May 25 2011
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