A191019 Rational primes that decompose in the quadratic field Q(sqrt(-19)).

5, 7, 11, 17, 23, 43, 47, 61, 73, 83, 101, 131, 137, 139, 149, 157, 163, 191, 197, 199, 229, 233, 239, 251, 263, 271, 277, 283, 311, 313, 347, 349, 353, 359, 367, 389, 397, 419, 443, 457, 461, 463, 467, 479, 491, 499, 503, 541, 557, 571, 577, 587, 593, 613

Offset

1,1

Comments

Primes which are 1, 5, 7, 9, 11, 17, 23, 25, or 35 mod 38. - Charles R Greathouse IV, Mar 18 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index to sequences related to decomposition of primes in quadratic fields

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Mar 18 2018

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#, 19]==1&]

Prog

(Magma) [p: p in PrimesUpTo(613) | IsOne(JacobiSymbol(p, 19))]; // Bruno Berselli, Sep 10 2012
(PARI) list(lim)=my(v=List()); forprime(p=5, lim, if(kronecker(-19, p)==1, listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Mar 18 2018

Crossrefs

Sequence in context: A191080 A293200 A067830 * A106862 A027690 A087200

Adjacent sequences: A191016 A191017 A191018 * A191020 A191021 A191022

Keyword

nonn,easy

Author

T. D. Noe, May 24 2011

Extensions

Definition corrected by N. J. A. Sloane, Dec 25 2017

Status

approved