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A139847 Primes of the form 6x^2 + 6xy + 19y^2. 2
19, 31, 139, 199, 271, 439, 619, 691, 811, 859, 1039, 1231, 1279, 1291, 1399, 1459, 1531, 1699, 1879, 1951, 2131, 2239, 2371, 2539, 2551, 2659, 2719, 2791, 2971, 3079, 3331, 3391, 3499, 3559, 3631, 3919, 4051, 4219, 4231, 4339, 4591, 4639 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = -420. See A139827 for more information.

Also primes of the forms 19x^2 + 12xy + 24y^2 and 19x^2 + 16xy + 31y^2. See A140633. - T. D. Noe, May 19 2008

LINKS

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

FORMULA

The primes are congruent to {19, 31, 139, 199, 271, 391} (mod 420).

MATHEMATICA

QuadPrimes2[6, -6, 19, 10000] (* see A106856 *)

PROG

(Magma) [ p: p in PrimesUpTo(6000) | p mod 420 in {19, 31, 139, 199, 271, 391}]; // Vincenzo Librandi, Jul 29 2012

(PARI) list(lim)=my(v=List(), s=[19, 31, 139, 199, 271, 391]); forprime(p=19, lim, if(setsearch(s, p%420), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

CROSSREFS

Sequence in context: A237418 A240126 A125602 * A087764 A146691 A146784

Adjacent sequences: A139844 A139845 A139846 * A139848 A139849 A139850

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, May 02 2008

STATUS

approved

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Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)