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A141785 Primes of the form -x^2+5*x*y+5*y^2 (as well as of the form 9*x^2+15*x*y+5*y^2). 6
5, 11, 29, 41, 59, 71, 89, 101, 131, 149, 179, 191, 239, 251, 269, 281, 311, 359, 389, 401, 419, 431, 449, 461, 479, 491, 509, 521, 569, 599, 641, 659, 701, 719, 761, 809, 821, 839, 881, 911, 929, 941, 971, 1019, 1031, 1049, 1061, 1091, 1109, 1151, 1181, 1229, 1259 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = 45. Class = 2. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1

REFERENCES

Borevich and Shafaewich, Number Theory.

D. B. Zagier, Zetafunktionen und quadratische Koerper.

LINKS

Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000

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

EXAMPLE

a(2)=29 because we can write 29=-1^2+5*1*2+5*2^2 (or 29=9*1^2+15*1*1+5*1^2)

MATHEMATICA

Select[Prime[Range[250]], # == 5 || MatchQ[Mod[#, 45], Alternatives[11, 14, 26, 29, 41, 44]]&] (* Jean-Fran├žois Alcover, Oct 28 2016 *)

CROSSREFS

Cf. A033212 (d=45), A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).

For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Sequence in context: A019345 A049489 A242383 * A144311 A074367 A088486

Adjacent sequences:  A141782 A141783 A141784 * A141786 A141787 A141788

KEYWORD

nonn

AUTHOR

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008

STATUS

approved

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Last modified December 5 11:48 EST 2016. Contains 278765 sequences.