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

Author

T. D. Noe, May 24 2011

Keywords

• nonn
• easy

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

Programs

Magma

[p: p in PrimesUpTo(613) | IsOne(JacobiSymbol(p, 19))]; // Bruno Berselli, Sep 10 2012

Mathematica

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

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

Formula

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

Extensions

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