

A191017


Primes with Kronecker symbol (p14) = 1.


20



3, 5, 13, 19, 23, 59, 61, 71, 79, 83, 101, 113, 127, 131, 137, 139, 151, 157, 173, 181, 191, 193, 227, 229, 233, 239, 251, 263, 269, 281, 283, 293, 307, 337, 349, 359, 397, 401, 419, 431, 449, 457, 461, 463, 467, 487, 509, 523, 563, 569, 587, 599, 617, 619
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OFFSET

1,1


COMMENTS

Originally incorrectly named "Primes that are squares mod 14", which is sequence A045373.  M. F. Hasler, Jan 15 2016
Conjecture: primes congruent to {1, 3, 5, 9, 13, 15, 19, 23, 25, 27, 39, 45} mod 56.  Vincenzo Librandi, Jun 22 2016
Rational primes that decompose in the field Q(sqrt(14)).
These are primes p such that either one of (a) p == 1, 2, 4 (mod 7), p == 1, 7 (mod 8) or (b) p == 3, 5, 6 (mod 7), p == 3, 5 (mod 8) holds. So the conjecture above is correct. (End)


LINKS



MATHEMATICA

Select[Prime[Range[200]], JacobiSymbol[#, 14]==1&]


PROG

(Magma) [p: p in PrimesUpTo(619)  KroneckerSymbol(p, 14) eq 1]; // Vincenzo Librandi, Sep 11 2012


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



