login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A141183 Primes of the form -x^2+6*x*y+2*y^2 (as well as of the form 7*x^2+10*x*y+2*y^2). 8
2, 7, 11, 19, 43, 79, 83, 107, 127, 131, 139, 151, 167, 211, 227, 239, 263, 271, 283, 307, 347, 359, 431, 439, 479, 491, 503, 523, 547, 563, 571, 607, 659, 739, 743, 787, 811, 827, 887, 919, 967, 1019, 1031, 1051, 1063, 1091, 1151, 1163, 1187, 1223, 1231, 1283, 1319, 1327 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = 44. 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.

Also primes of form 11*u^2-v^2. The transformation {u,v}={-3*x-y,10*x+3*y} yields the form in the title. - Juan Arias-de-Reyna Mar 20 2011.

Also primes p equal -1 mod 4 and = 1, 3, 4, 5, or 9  mod 11. - Juan Arias-de-Reyna Mar 20 2011.

REFERENCES

Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, NY, 1966.

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(4)=19 because we can write 19= -1^2+6*1*2+2*2^2 (or 19=7*1^2+10*1*1+2*1^2).

MATHEMATICA

Select[Prime[Range[250]], # == 2 || # == 11 || MatchQ[Mod[#, 44], Alternatives[7, 19, 35, 39, 43]]&] (* Jean-Fran├žois Alcover, Oct 28 2016 *)

CROSSREFS

Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A141182 (d=44).

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: A106905 A097159 A139603 * A308724 A103182 A160698

Adjacent sequences:  A141180 A141181 A141182 * A141184 A141185 A141186

KEYWORD

nonn

AUTHOR

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (sergarmor(AT)yahoo.es), Jun 13 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 5 03:58 EDT 2020. Contains 333238 sequences. (Running on oeis4.)